Some combinatorial aspects of discrete non-linear population dynamics

Motivated by issues arising in population dynamics, we consider the problem of iterating a given analytic function a number of times. We use the celebrated technique known as Carleman linearization that turns (for a certain class of functions) this problem into simply taking the power of a real number. We expand this method, showing in particular that it can be used for population models with immigration, and we also apply it to the famous logistic map. We also are able to give a number of results for the invariant density of this map, some being related to the Carleman linearization.     

Stagnation-point flow past a shrinking sheet in a nanofluid

In this paper, the stagnation-point flow and heat transfer towards a shrinking sheet in a nanofluid is considered. The nonlinear system of coupled partial differential equations was transformed and reduced to a nonlinear system of coupled ordinary differential equations, which was solved numerically using the shooting method. Numerical results were obtained for the skin friction coefficient, the local Nusselt number as well as the velocity and temperature profiles for some values of the governing parameters, namely the nanoparticle volume fraction φ, the shrinking parameter λand the Prandtl number Pr. Three different types of nanoparticles are considered, namely Cu, Al₂O₃ and TiO₂. It was found that nanoparticles of low thermal conductivity, TiO₂, have better enhancement on heat transfer compared to nanoparticles Al₂O₃ and Cu. For a particular nanoparticle, increasing the volume fraction φ results in an increase of the skin friction coefficient and the heat transfer rate at the surface. It is also found that solutions do not exist for larger shrinking rates and dual solutions exist when λ < −1.0.     

三种生成神经网络拓扑结构的方法在股票、商品价格预测中的应用及结果比较

对比了三种不同神经网络模型的生成方式:传统神经网络生成模型,遗传算法训练神经网络模型,以及在第二种方式训练参数的基础上,再使用传统神经网络优化生成模型.论文使用上述三种方法对代表性股票和商品价格进行拟合并预测,通过预测结果准确性和稳定性的比较发现:引入遗传算法后的神经网络在样本内的拟合误差有所降低,而第三种方法在样本外有最低的预测误差和最优稳定性.     

Three-dimensional rotating flow induced by a shrinking sheet for suction

Series solution of magnetohydrodynamic (MHD) and rotating flow over a porous shrinking sheet is obtained by a homotopy analysis method (HAM). The viscous fluid is electrically conducting in the presence of a uniform applied magnetic field and the induced magnetic field is neglected for small magnetic Reynolds number. Similarity solutions of coupled non-linear ordinary differential equations resulting from the momentum equation are obtained. Convergence of the obtained solutions is ensured by the proper choice of auxiliary parameter. Graphs are sketched and discussed for various emerging parameters on the velocity field. The variations of the wall shear stress f″(0) and ?g′(0) are also tabulated and analyzed.     

Global dynamics and cost-effectiveness analysis of HIV pre-exposure prophylaxis and structured treatment interruptions based on a multi-scale model

Structured treatment interruptions (STI) were proposed to reduce costs and side effects for HIV infected individuals, but whether the possible viral rebound within hosts after treatment interruption would lead to more new infections and additional costs among the population remains unknown. Oral pre-exposure prophylaxis (PrEP) is shown as an effective but expensive strategy to prevent the acquisition of HIV infection. To investigate the effectiveness and cost-effectiveness of STI and PrEP, we develop a multi-scale model linking within-host and between-host dynamics in the presence of drug resistance. Lyapunov functionals are constructed to analyze the global dynamics of the coupled system. We fit this model to the annual AIDS incidence and death data from 1980 to 2014 among men who have sex with men (MSM) in San Francisco and compare the impact of six various intervention scenarios (low, medium, high PrEP coverage with or without STI) on new infections and cost-effectiveness over the next 20 years. We estimate the PrEP efficacy needed to eliminate the disease for different fraction of acquired drug resistance under the above six scenarios. Numerical simulations show that expanding PrEP coverage is very cost-effective, but whether implementing STI is cost-saving depends on the efficacy of second-line drugs. That is to say, STI could always save money, but it may lead to more (less) new infections than continuous therapy and thus less (more) health benefit for high (low) efficacy of second-line drugs. These results provide insights about the long-term effect of STI and PrEP on the disease control and cost-effectiveness.     

Computing complex and real tropical curves using monodromy

Tropical varieties capture combinatorial information about how coordinates of points in a classical variety approach zero or infinity. We present algorithms for computing the rays of a complex and real tropical curve defined by polynomials with constant coefficients. These algorithms rely on homotopy continuation, monodromy loops, and Cauchy integrals. Several examples are presented which are computed using an implementation that builds on the numerical algebraic geometry software Bertini.     

Lanczos method for large-scale quaternion singular value decomposition

In many color image processing and recognition applications, one of the most important targets is to compute the optimal low-rank approximations to color images, which can be reconstructed with a small number of dominant singular value decomposition (SVD) triplets of quaternion matrices. All existing methods are designed to compute all SVD triplets of quaternion matrices at first and then to select the necessary dominant ones for reconstruction. This way costs quite a lot of operational flops and CPU times to compute many superfluous SVD triplets. In this paper, we propose a Lanczos-based method of computing partial (several dominant) SVD triplets of the large-scale quaternion matrices. The partial bidiagonalization of large-scale quaternion matrices is derived by using the Lanczos iteration, and the reorthogonalization and thick-restart techniques are also utilized in the implementation. An algorithm is presented to compute the partial quaternion singular value decomposition. Numerical examples, including principal component analysis, color face recognition, video compression and color image completion, illustrate that the performance of the developed Lanczos-based method for low-rank quaternion approximation is better than that of the state-of-the-art methods.

     

Mutual rankings

This paper analyzes some ranking methods in two-sided settings through their axiomatization. In these settings, there are two sets (the sides) and each member of one side evaluates each member of the other side. Such settings with mutual evaluations abound, for instance between buyers and sellers, students and teachers, or individuals and clubs.     

Evolutionary games with facilitators: When does selection favor cooperation?

We study the combined influence of selection and random fluctuations on the evolutionary dynamics of two-strategy (“cooperation” and “defection”) games in populations comprising cooperation facilitators. The latter are individuals that support cooperation by enhancing the reproductive potential of cooperators relative to the fitness of defectors. By computing the fixation probability of a single cooperator in finite and well-mixed populations that include a fixed number of facilitators, and by using mean field analysis, we determine when selection promotes cooperation in the important classes of prisoner’s dilemma, snowdrift and stag-hunt games. In particular, we identify the circumstances under which selection favors the replacement and invasion of defection by cooperation. Our findings, corroborated by stochastic simulations, show that the spread of cooperation can be promoted through various scenarios when the density of facilitators exceeds a critical value whose dependence on the population size and selection strength is analyzed. We also determine under which conditions cooperation is more likely to replace defection than vice versa.     

A newton approach for long term stability studies in power systems

This paper deals with the problem of transient and long term stability of power systems. The issue of assessing both horizons of analysis is particularly focused. This is because the long term stability may be studied by a simplified algebraic model which also captures some dynamic characteristics. Such an approach is called quasi-dynamic model. The idea of analyzing the transient period and migrating to the quasi-dynamic model is addressed in this paper. The theoretical foundation is presented and some tests are carried out in order to validate the approach.