Homotopy algorithms for solving structured determinantal systems

Multivariate polynomial systems arising in numerous applications have special structures. In particular, determinantal structures and invariant systems appear in a wide range of applications such as in polynomial optimization and related questions in real algebraic geometry. The goal of this thesis is to provide efficient algorithms to solve such structured systems. In order to solve the first kind of systems, we design efficient algorithms by using the symbolic homotopy continuation techniques. While the homotopy methods, in both numeric and symbolic, are well-understood and widely used in polynomial system solving for square systems, the use of these methods to solve over-detemined systems is not so clear. Meanwhile, determinantal systems are over-determined with more equations than unknowns. We provide probabilistic homotopy algorithms which take advantage of the determinantal structure to compute isolated points in the zero-sets of determinantal systems. The runtimes of our algorithms are polynomial in the sum of the multiplicities of isolated points and the degree of the homotopy curve. We also give the bounds on the number of isolated points that we have to compute in three contexts: all entries of the input are in classical polynomial rings, all these polynomials are sparse, and they are weighted polynomials. In the second half of the thesis, we deal with the problem of finding critical points of a symmetric polynomial map on an invariant algebraic set. We exploit the invariance properties of the input to split the solution space according to the orbits of the symmetric group. This allows us to design an algorithm which gives a triangular description of the solution space and which runs in time polynomial in the number of points that we have to compute. Our results are illustrated by applications in studying real algebraic sets defined by invariant polynomial systems by the means of the critical point method

New Algorithms for Balancing Energy Consumption and Performance in Computational Clusters

In this paper, we propose new real-time measurement-based scheduling algorithms to achieve a trade-off between the energy efficiency and the performance capability of computational clusters. An investigation is performed using a specific scenario of computing clusters with realistic parameters. Numerical results show that a trade-off between the performance and the energy efficiency can be controlled by the proposed algorithms

The Role of Social Network Sites in English Language Teaching_Harnessing the Potential of Facebook and YouTube as Learning Tools

This paper provides a comprehensive review of the role of Social Network Sites (SNSs) in the context of English as a Second Language (ESL) and English as a Foreign Language (EFL) teaching and learning. It examines the definitions and potential applications of SNSs, with a specific focus on Facebook and YouTube. The paper discusses the educational and instructional implementations of these SNSs, as well as the challenges and drawbacks faced by both teachers and students when utilizing them. Furthermore, it explores the pedagogical implications of incorporating the cutting-edge features offered by SNSs, aiming to bridge the gap between traditional and technologically driven learning environment

Some Overviews on Organic Agriculture Apply Circular Economy

The paper provides an overview on agriculture apply circular economy (CE). It provides the concepts of circular economy and organic agriculture. The paper used secondary researches from topics, documents related to organic agriculture apply CE. With results which the previous studies mentioned, the paper bases on different CE theoretical approaches to clarify the concept of organic agriculture in the direction of circular economy. Keywords: organic agriculture, circular economy DOI: 10.7176/JESD/13-20-01 Publication date:October 31st 202

REALIZATION OF BROADBAND AND INDEPENDENT POLARIZATION METAMATERIAL PERFECT ABSORBER BASED ON THE THIRD-ORDER RESONANCE

In this report, we studied numerically and experimentally the electromagnetic properties of perfect MAs using ring-shaped structures at microwave frequencies. By creating a magnetic resonance, the ring structure confines electromagnetic energy at the first- and third-order resonances. And then, we leveraged the super-cell structures, which consist of different rings in one unit cell to obtain broadband absorption. The results showed that the absorption band of MA is broaden from 1.3 to 2.17 GHz when the number of rings in the unit cell increases from four to nine-ring

Robust adaptive controller for wheel mobile robot with disturbances and wheel slips

In this paper an observer based adaptive control algorithm is built for wheel mobile robot (WMR) with considering the system uncertainties, input disturbances, and wheel slips. Firstly, the model of the kinematic and dynamic loops is shown with presence of the disturbances and system uncertainties. Next, the adaptive controller for nonlinear mismatched disturbance systems based on the disturbances observer is presented in detail. The controller includes two parts, the first one is for the stability purpose and the later is for the disturbances compensation. After that this control scheme is applied for both two loops of the system. In this paper, the stability of the closed system which consists of two control loops and the convergence of the observers is mathematically analysed based on the Lyapunov theory. Moreover, the proposed model does not require the complex calculation so it is easy for the implementation. Finally, the simulation model is built for presented method and the existed one to verify the correctness and the effectiveness of the proposed scheme. The simulation results show that the introduced controller gives the good performances even that the desired trajectory is complicated and the working condition is hard

Homotopy techniques for solving sparse column support determinantal polynomial systems

Let $\mathbf{K}$ be a field of characteristic zero with $\overline{\mathbf{K}}$ its algebraic closure. Given a sequence of polynomials $\mathbf{g} = (g_1, \ldots, g_s) \in \mathbf{K}[x_1, \ldots , x_n]^s$ and a polynomial matrix $\mathbf{F} = [f_{i,j}] \in \mathbf{K}[x_1, \ldots, x_n]^{p \times q}$, with $p \leq q$, we are interested in determining the isolated points of $V_p(\mathbf{F},\mathbf{g})$, the algebraic set of points in $\overline{\mathbf{K}}$ at which all polynomials in $\mathbf{g}$ and all $p$-minors of $\mathbf{F}$ vanish, under the assumption $n = q - p + s + 1$. Such polynomial systems arise in a variety of applications including for example polynomial optimization and computational geometry. We design a randomized sparse homotopy algorithm for computing the isolated points in $V_p(\mathbf{F},\mathbf{g})$ which takes advantage of the determinantal structure of the system defining $V_p(\mathbf{F}, \mathbf{g})$. Its complexity is polynomial in the maximum number of isolated solutions to such systems sharing the same sparsity pattern and in some combinatorial quantities attached to the structure of such systems. It is the first algorithm which takes advantage both on the determinantal structure and sparsity of input polynomials. We also derive complexity bounds for the particular but important case where $\mathbf{g}$ and the columns of $\mathbf{F}$ satisfy weighted degree constraints. Such systems arise naturally in the computation of critical points of maps restricted to algebraic sets when both are invariant by the action of the symmetric group

Applying means-end chain theory and laddering interviews to the study of product attributes for Dalat potatoes

Dalat potato brand has currently been facing unfair competition from wholesalers using Chinese potatoes labeled with Vietnamese brand to disguise their true origin. Accordingly, potatoes from China are first transported to Lam Dong and then covered by Lam Dong soil to cheat consumers. This study, therefore, aims to explore key attributes of Dalat potatoes, and the benefits and values created by these attributes for consumers of Dalat potatoes. In order to address the research objective, the study uses a qualitative approach based on means-end chain theory and laddering interviews to collect and analyze the data. Eventually, the linkage between attributes, consequences and values are established to help governmental authorities of Lam Dong province to develop strategies for promoting Dalat potato brand. The finding shows that ‘High food value’, ‘Trustful product’ and ‘Tasty and greasy taste’ are key attributes of Dalat potatoes. The linkage between potatoes attributes, benefits and values show that consuming good farm produce like Dalat potatoes help consumers enjoy a better life. This is essential for authorities to position and build a more solid brand for this specialty. To conclude, the paper discusses some managerial implications for promoting and branding Dalat potatoes