A Novel PSO Model Based on Simulating Human Social Communication Behavior

In order to solve the complicated multimodal problems, this paper presents a variant of particle swarm optimizer (PSO) based on the simulation of the human social communication behavior (HSCPSO). In HSCPSO, each particle initially joins a default number of social circles (SC) that consist of some particles, and its learning exemplars include three parts, namely, its own best experience, the experience of the best performing particle in all SCs, and the experiences of the particles of all SCs it is a member of. The learning strategy takes full advantage of the excellent information of each particle to improve the diversity of the swarm to discourage premature convergence. To weight the effects of the particles on the SCs, the worst performing particles will join more SCs to learn from other particles and the best performing particles will leave SCs to reduce their strong influence on other members. Additionally, to insure the effectiveness of solving multimodal problems, the novel parallel hybrid mutation is proposed to improve the particle’s ability to escape from the local optima. Experiments were conducted on a set of classical benchmark functions, and the results demonstrate the good performance of HSCPSO in escaping from the local optima and solving the complex multimodal problems compared with the other PSO variants

New Region-Scalable Discriminant and Fitting Energy Functional for Driving Geometric Active Contours in Medical Image Segmentation

We propose a novel region-based geometric active contour model that uses region-scalable discriminant and fitting energy functional for handling the intensity inhomogeneity and weak boundary problems in medical image segmentation. The region-scalable discriminant and fitting energy functional is defined to capture the image intensity characteristics in local and global regions for driving the evolution of active contour. The discriminant term in the model aims at separating background and foreground in scalable regions while the fitting term tends to fit the intensity in these regions. This model is then transformed into a variational level set formulation with a level set regularization term for accurate computation. The new model utilizes intensity information in the local and global regions as much as possible; so it not only handles better intensity inhomogeneity, but also allows more robustness to noise and more flexible initialization in comparison to the original global region and regional-scalable based models. Experimental results for synthetic and real medical image segmentation show the advantages of the proposed method in terms of accuracy and robustness

The Existence of Invariant Tori and Quasiperiodic Solutions of the Nosé–Hoover Oscillator

In this paper, we consider an equivalent form of the Nosé–Hoover oscillator, x′=y,y′=−x−yz, and z′=y2−a, where a is a positive real parameter. Under a series of transformations, it is transformed into a 2-dimensional reversible system about action-angle variables. By applying a version of twist theorem established by Liu and Song in 2004 for reversible mappings, we find infinitely many invariant tori whenever a is sufficiently small, which eventually turns out that the solutions starting on the invariant tori are quasiperiodic. The discussion about quasiperiodic solutions of such 3-dimensional system is relatively new

Global structure of solutions to boundary-value problems of impulsive differential equations

In this article, we study the structure of global solutions to the boundary-value problem \displaylines{ -x''(t)+f(t,x)=\lambda ax(t),\quad t\in(0,1),\; t\neq\frac{1}{2},\cr \Delta x|_{t=1/2}=\beta_1 x(\frac{1}{2}),\quad \Delta x'|_{t=1/2}=-\beta_{2} x(\frac{1}{2}),\cr x(0)=x(1)=0, } where $\lambda\neq0$, $\beta_1\geq\beta_{2}\geq0$, $\Delta x|_{t=1/2}=x(\frac{1}{2}+0)-x(\frac{1}{2})$, $\Delta x'|_{t=1/2}=x'(\frac{1}{2}+0)-x'(\frac{1}{2}-0)$, and $f:[0,1]\times\mathbb{R}\to\mathbb{R}$, $a:[0,1]\to(0,+\infty)$ are continuous. By a comparison principle and spectral properties of the corresponding linear equations, we prove the existence of solutions by using Rabinowitz-type global bifurcation theorems, and obtain results on the behavior of positive solutions for large $\lambda$ when $f(x)=x^{p+1}$

Multi-Output Based Hybrid Integrated Models for Student Performance Prediction

In higher education, student learning relies increasingly on autonomy. With the rise in blended learning, both online and offline, students need to further improve their online learning effectiveness. Therefore, predicting students’ performance and identifying students who are struggling in real time to intervene is an important way to improve learning outcomes. However, currently, machine learning in grade prediction applications typically only employs a single-output prediction method and has lagging issues. To advance the prediction of time and enhance the predictive attributes, as well as address the aforementioned issues, this study proposes a multi-output hybrid ensemble model that utilizes data from the Superstar Learning Communication Platform (SLCP) to predict grades. Experimental results show that using the first six weeks of SLCP data and the Xgboost model to predict mid-term and final grades meant that accuracy reached 78.37%, which was 3–8% higher than the comparison models. Using the Gdbt model to predict homework and experiment grades, the average mean squared error was 16.76, which is better than the comparison models. This study uses a multi-output hybrid ensemble model to predict how grades can help improve student learning quality and teacher teaching effectiveness

The existence of positive solutions for the singular two-point boundary value problem

In this paper, we consider the following boundary value problem: $$\begin{cases} ((-u'(t))^n)'=nt^{n-1}f(u(t)) &\text{for }0< t< 1,\\ u'(0)=0,\quad u(1)=0, \end{cases}$$% where n> 1. Using the fixed point theory on a cone and approximation technique, we obtain the existence of positive solutions in which $f$ may be singular at $u=0$ or $f$ may be sign-changing