Leslie Matrix Research Articles

Leslie matrix matching approach in labor market studies

Leslie matrix matching approach in labor market studies

Approximation of the long-time dynamics of the dynamical system generated by the Ericksen–Leslie equations

In this article we study the long-time dynamics of the dynamical system generated by the Ericksen–Leslie model. More precisely, we discretize the Ericksen–Leslie equations in time using the implicit Euler scheme, and with the aid of the discrete Gronwall lemmas we prove that the scheme is uniformly bounded. Moreover, using the theory of the multi-valued attractors we prove in a particular case the convergence of the global attractors generated by the numerical scheme to the global attractor of the continuous system as the time-step approaches zero.

Leslie Matrix Model For Euphorbia Hirta L Population

Invasive species management has developed into a highly specialized field utilizing a systems approach. It requires knowledge of their life history, growth requirements, and population dynamics that integrate their biology and control. The foundation of strategic planning for the management of invasive species is laid by demographic studies, which record the birth, growth, reproduction, and death of individuals within a population. The present study makes use of the Discrete Leslie Matrix Model to analyze the growth in the age-structured population of Euphorbia hirta, an invasive species in agrosystems, identify critical stages in the species' life cycle, and project the structure and size of future population.

Evaluation of potential factors affecting the success of Cisco re-introduction and re-establishment in Lake Huron

Recent food web changes led to an opportunity to reintroduce (fingerling stocking) Cisco in central Lake Huron. We examined 9 factors affecting the ability of stocked Cisco fingerlings to survive, and reproduce and for their progeny to survive and reproduce. These values (obtained from the literature) were applied to a stochastic Leslie Matrix model and projected forward 30 years. The mean terminal eigenvalue (λ) of the final 10 years was used to indicate if the resulting wild population would continue to increase or decrease and thresholds for each variable. Recovery success was sensitive to survival rates especially in early life stages. Numbers stocked and the rate of homing by hatchery fish only affected the rate of recovery. Adult survival, if adjusted up, helped compensate for many of the earlier life stages lower survival rates. Simulations indicated the likelihood of successful establishment of ongoing natural reproduction if periodicity of boom years of reproduction were at least once every 5 years on average, but higher adult survival rates can relax this requirement allowing for an expanding population at less frequent periodicities.

Характеристики демографічної резильєнтності населення України у період пандемії Covid-19

The full-scale military invasion of Ukraine by the Russian Federation came at a time when our country had been weakened by a series of shocks in a relatively short historical period. Shocks such as a prolonged pandemic and war can disrupt and, in some cases, halt demographic development. In this context, the study of demographic resilience on the eve of a full-scale war, which became a new powerful shock for Ukraine, is relevant and necessary. The complexity of this issue does not allow us to provide all the answers in one article. The purpose of our paper is to determine the main parameters of the demographic resilience of the population of Ukraine in the Covid-19 period and to compare them with the characteristics of resilience in other periods of the greatest shocks experienced by our country, as well as with the indicators of other countries. In our study the main indicators of transient dynamics (convergence time, reactivity, population inertia, damping ratio) were calculated for the first time for the population of Ukraine. The influence of the contribution of different age groups of women to total fertility on the age structure of the population (with the same total fertility rate) was also determined for the first time. The calculations were based on the stable population model, the Leslie matrix, fertility tables, and life tables. The resilience indicators were calculated using the popdemo package. Methods of comparison, generalisation, and analogy were also used. Among the characteristics of demographic resilience, the half-life indicator stands out for its simplicity of calculation and interpretation. In Ukraine, the halving time for the population is decreasing, but it is still higher for the real population than for its stable equivalent. The age structure of the real population, formed under more favourable conditions, mitigates the negative consequences of shock periods, but the long-term preservation of the current regime of mortality and fertility will inevitably worsen the characteristics of the population. In Ukraine, advanced motherhood is an element of the adaptive cycle and requires a rethinking of its meaning and role, as it can be one of the internal mechanisms aimed at the resilience of the system in shock periods. In the conditions of the lowest-low fertility and mortality regime in Ukraine in 2021, advanced maternal age contributed to some increase in the number of births and a certain rejuvenation of the age structure of the population.

Applications of Matrix Multiplication

In this paper we present some interesting applications of the matrix’s multiplication, that include the Leslie matrix and population change, which we calculate this kind of changes from year to other year by matrix multiplication. Another important part of the paper is Analysis of Traffic Flow, we represent the flow of traffic through a network of one-way streets. Another much important part is the production costs, this is fantastic usage of matrix multiplication, in which, A company manufactures three products. Its production expenses are divided into three categories, here in this paper we well describe this beautiful issue. By matrix multiplication, we can encode and decode messages. To encode a message, we choose an invertible matrix and multiply the uncoded row matrices (on the right) by to obtain coded row matrices, this idea will be clarify by some useful examples. Also we used to study certain relationships between objects by matrix multiplication. We will clarify all of these applications by useful examples. In this paper, we present six different applications of matrix multiplication.

Various Comparative Studies of Constantly Applied Methods in Assisting the Demography Research of China

Demography research is of great importance due to it can affect various aspects of a country. We mainly focus on using various comparative studies to examine and predict the population quantity, female size, and urban population size of China. We initially compared the effectiveness of several interpolation algorithms to add more samples and then we constructed two more comparative studies of the Malthus model, Logistic model, GM (1, 1) model, BP neural network, and Leslie model to assist the demography research of China. Especially, three novel metaheuristic algorithms were applied to the Logistic model. Compared results verified that metaheuristics can assist the Logistic model to obtain far more accurate parameters and also revealed that using the Logistic model combined with a novel metaheuristic to predict the population quantity and urban population size and the BP neural network to estimate the female size can acquire the most ideal results.

Constraint-preserved numerical schemes with decoupling structure for the Ericksen–Leslie model with variable density

In this paper, first- and second-order numerical schemes are developed for the Ericksen–Leslie model with variable density. The influence of variable density leads to some conflicts between decoupling and unconditional energy stability. We overcome it by special discretization and extra-fractional-step method. The fully decoupled structures are obtained by using the scalar auxiliary variable (SAV) method with only one SAV. This allows only one additional ODE to be solved so that the schemes are computationally cheaper. The non-convex constraint |b|=1 is preserved by rewriting the orientation field with polar coordinates. It also improves computational efficiency because the vector function of the orientation field is replaced by scalar function. We first reformulate the Ericksen–Leslie model as an equivalent new form by introducing a SAV and polar coordinate form of the orientation field. Secondly, two linear schemes and the corresponding unconditional energy stabilities are established. Then, we show the detailed implementations for proving that the schemes are fully decoupled and uniquely solvable. Finally, the convergence rates and energy dissipations are tested by performing some numerical experiments. The evolutionary simulations are also given.

Modeling the Impact of Lamprey Population Dynamics on Aquatic Food Webs: A Leslie and Lotka-Volterra Approach

In recent years, the widely distributed invasive parasitic species of marine lampreys have had a profound impact on host populations and the entire aquatic ecosystem through their unique survival and reproduction strategies, highlighting the importance of species interactions and ecological balance in ecosystems. In response to this, this study establishes a species growth model for lampreys based on the Leslie model from the perspective of gender ratio changes. The idea of the Lotka-Volterra predator-prey model is used to establish the food web centered on lamprey and the fluctuation mode model of various groups in it. Based on the model results, we conclude that the growth trend of the lamprey itself is difficult to be affected by other populations, but the lamprey population will have serious adverse effects on other species. The results of this model are in good agreement with the actual situation, and have profound significance in laying the foundation for the study of the community characteristics of lampreys and their related ecosystems.

Projection of Interspecific Competition (PIC) Matrices: A Conceptual Framework for Inclusion in Population Risk Assessments.

Accounting for intraspecific and interspecific competition when assessing the effects of chemical and nonchemical stressors is an important uncertainty in ecological risk assessments. We developed novel projection of interspecific competition (PIC) matrices that allow for analysis of population dynamics of two or more species exposed to a given stressor(s) that compete for shared resources within a landscape. We demonstrate the application of PIC matrices to investigate the population dynamics of two hypothetical fish species that compete with one another and have differences in net reproductive rate and intrinsic rate of population increase. Population status predictions were made under scenarios that included exposure to a chemical stressor that reduced fecundity for one or both species. The results of our simulations demonstrated that measures obtained from the life table and Leslie matrix of an organism, including net reproductive rate and intrinsic rate of increase, can result in erroneous conclusions of population status and viability in the absence of a consideration of resource limitation and interspecific competition. This modeling approach can be used in conjunction with field monitoring efforts and/or laboratory testing to link effects due to stressors to possible outcomes within an ecosystem. In addition, PIC matrices could be combined with adverse outcome pathways to allow for ecosystem projection based on taxonomic conservation of molecular targets of chemicals to predict the likelihood of relative cross-species susceptibility. Overall, the present study shows how PIC matrices can integrate effects across the life cycles of multiple species, provide a linkage between endpoints observed in individual and population-level responses, and project outcomes at the community level for multiple generations for multiple species that compete for limited resources. Environ Toxicol Chem 2024;43:1406-1422. Published 2024. This article is a U.S. Government work and is in the public domain in the USA.

Prediction Of Population Size and Age Structure in China Based on Grey Prodiction and Leslie Model

Population is a major problem that restricts China's comprehensive, coordinated and sustainable development. Therefore, it is of great significance to establish a model that can accurately predict the population and age structure. This paper uses GM (1,1) to obtain the gender ratio of future newborn population and total population, quantifies the three-child policy as the increase in the fertility rate of women of childbearing age, uses the Leslie model to obtain the female population at all ages, and finally gets the national population and age structure in the next five years under the background of the three-child policy. The results show that the opening of the three-child policy positively impacts the increase of the newborn population and the growth rate of the total population in the early future. But as time goes by, it still cannot restrain the decrease in the newborn population and the net increase of the total population. In addition, the aging problem has not been effectively improved in the short term. In the next five years, the proportion of the aged population continues to rise, while the young population gradually decreases. In terms of the labor force coefficient, there will be a downward trend from 2021 to 2025 and a slight increase from 2025 to 2026.

Prediction Of Population Size and Age Structure in China Based on Grey Prodiction and Leslie Model

Population is a major problem that restricts China's comprehensive, coordinated and sustainable development. Therefore, it is of great significance to establish a model that can accurately predict the population and age structure. This paper uses GM (1,1) to obtain the gender ratio of future newborn population and total population, quantifies the three-child policy as the increase in the fertility rate of women of childbearing age, uses the Leslie model to obtain the female population at all ages, and finally gets the national population and age structure in the next five years under the background of the three-child policy. The results show that the opening of the three-child policy positively impacts the increase of the newborn population and the growth rate of the total population in the early future. But as time goes by, it still cannot restrain the decrease in the newborn population and the net increase of the total population. In addition, the aging problem has not been effectively improved in the short term. In the next five years, the proportion of the aged population continues to rise, while the young population gradually decreases. In terms of the labor force coefficient, there will be a downward trend from 2021 to 2025 and a slight increase from 2025 to 2026.

LESLIE MATRIX CONSTRUCTION AND ITS PROPERTIES IN PREDICTING THE SIZE OF THE FEMALE POPULATION

The growth of the female population needs to be considered because if the female population is not controlled, it is feared that it could trigger a population explosion. Using the Leslie matrix, this study aimed to predict the number and growth rate of the female population in Batugajah Village, Mdona Hyera Subdistrict, Southwest Maluku Regency. Based on the results of the study, the female population in Batugajah Village, Mdona Hyera Subdistrict, Southwest Maluku Regency, is predicted to be 157 people in 2021, 150 people in 2022, and 142 people in 2023. Furthermore, the most significant positive eigenvalue is 0.6521, which indicates that the population growth rate will tend to decrease.

Initial-Boundary Value Problems for Poiseuille Flow of Nematic Liquid Crystal via Full Ericksen–Leslie Model

Initial-Boundary Value Problems for Poiseuille Flow of Nematic Liquid Crystal via Full Ericksen–Leslie Model

The Second-Order Numerical Approximation for a Modified Ericksen–Leslie Model

In this study, two numerical schemes with second-order accuracy in time for a modified Ericksen–Leslie model are constructed. The highlight is based on a novel convex splitting method for dealing with the nonlinear potentials, which is integrated with the second-order backward differentiation formula (BDF2) and leap frog method for temporal discretization and the finite element method for spatial discretization. The unconditional energy stability of both schemes is further demonstrated. Finally, several numerical examples are presented to demonstrate the efficiency and accuracy of the proposed schemes.

Onset of climate‐change impact on the renowned Oncorhynchus metapopulation of Yellowstone Lake revealed by Leslie modeling of annual gill‐net catches

AbstractThe native Yellowstone cutthroat trout (Oncorhynchus clarkii bouvieri; YCT) of Yellowstone Lake, Yellowstone National Park, Wyoming, USA, comprise a metapopulation that inhabits an ecologically simple and uniquely pristine environment. A recent study Bayesian fit an age‐structured Leslie model that had a local climate index (total annual mean‐daily air temperatures >0°C at the lake's north shore) as its only driver (regulating age‐0 YCT survival) to data for a key YCT spawning stock (median fish age, 5 years) from 1977 to 1992, before predation from an illegally introduced and growing lake trout (Salvelinus namaycush) population (1994 discovery) measurably affected YCT population dynamics. Results showed the new climate regime that began in the late 1970s had an overarching effect and largely explained declining spawning runs, although a growing predation effect became evident near lake trout discovery and quickly became the major YCT population driver. In the present study, that model was likewise fitted to estimated abundances of age‐5 YCT (~75% mature) that had been annually (also 1977–1992) gill‐netted from Yellowstone Lake and thus characterized the metapopulation. Results showed age‐0 YCT survival declined when a climate index of 1440 was reached and exceeded. Metapopulation recovery to historically high levels requires that the climate index decline to and remain near or below 1440 and—as shown by another recent study—that the lake trout population be reduced to its mid‐1990s levels. The most recent time of evident YCT metapopulation persistence at historically high levels and broadest spatial extent occurred under those simultaneous conditions.

Asymptotic Log-Harnack inequality for the 2D Ericksen–Leslie model system with degenerate noise and damping

In this paper, we consider a 2D liquid crystal model with damping and examine some asymptotic behaviors of the strong solution. More precisely, we establish the asymptotic log-Harnack inequality for the transition semigroup associated with a simplified liquid crystal model driven by an additive degenerate noise via the asymptotic coupling method. As consequences of the asymptotic log-Harnack inequality, we derive the gradient estimate, the asymptotic irreducibility, the asymptotic strong Feller property, the asymptotic heat kernel estimate and the ergodicity.

On bifurcations, resonances and dynamical behaviour in nonlinear iteroparous Leslie matrix models

Leslie matrix models with nonzero nonlinear fecundity elements are under consideration. It is proved that by use of the general Deriso–Schnute recruitment function the supercritical nature of bifurcations in 2- and 3-age class models and a thorough analysis of 1:2 and 1:3 resonance phenomena are also provided. A discussion of impact of coexisting attractors and structures of trapping regions is included as well. Results regarding stabilizing and destabilizing effects as well as dynamical outcomes found in general n-age class models are also presented. Suggestions with respect to where our models may apply are provided too.

Analisis Implementasi Matriks dalam Estimasi Laju Pertumbuhan Populasi Wanita

Leslie matrix is a growth matrix used to estimate the growth rate of a population. Through the population growth rate, information can be obtained whether the growth tends to increase, decrease, or stabilize. The general form of the Leslie matrix is a square matrix in which the first-row entries contain values of female fertility rate , the subdiagonals contain values of female survival rate , and entries other than in the first row and sub diagonals are zero. This research is to determine the implementation of the Leslie matrix in estimating the female population growth rate in Situbondo Regency 2023 and its analysis. The stages of this research began with presenting the Leslie matrix population growth model for the next three years. The second stage is to determine the age class interval. Next, determine the initial age distribution vector. The fourth and fifth stages, respectively, are calculating the and the value. The next step is constructing the Leslie matrix. The seventh stage is to calculate the estimated female population. The eighth stage is determining the eigenvalue and ends with determining the dominant eigenvalue. Based on the results of the research that has been done, it is obtained that the estimated female population in Situbondo Regency 2023 tends to decrease with the acquisition of a dominant eigenvalue that is less than one. That information can be taken into consideration by the government in formulating population-related policies.

Population Forecast and Analysis under China’s Three-Child Policy Based on the Leslie Model

Population Forecast and Analysis under China’s Three-Child Policy Based on the Leslie Model