Optimizing reserves in school choice: A dynamic programming approach

We introduce a new model of school choice with reserves in which asocial planner is constrained by a limited supply of reserve seats and tries to find the matching that is optimal according to a social welfare function. We construct the optimal distribution of reserves via a quartic-time dynamic programming algorithm. Due to the modular nature of the algorithm, the resulting mechanism is strategy-proof for reserve-eligible students.     

Win–win match using a genetic algorithm

As the service industries grow, tasks are not directly assigned to the skills but the knowledge of the worker which is to be valued more in finding the best match. The problem becomes difficult mainly because the match has to be seen with the objectives of both sides. Assignment methods fail to respond to a multi-objective, multi-constraint problem with complicated match; whereas, metaheuristics is preferable based on computational simplicity. A conditional genetic algorithm is developed in this study to propose both global and composite match using different fitness functions. This algorithm kills the infeasibilities to achieve the maximum number of matches. The proposed algorithm is applied on an academic problem of multi-alternative candidates and multi-alternative tasks (m × n problem) in two stages. In the first stage, four different fitness functions are evaluated and in the second stage using one of the fitness functions global and composite matching have been compared. The achievements will contribute both to the academic and business world.     

Influence of flat milling on vortex matching effect in Bi2Sr2CaCu2O8+y with antidot array

Significant enlargements of antidot diameter by Ar-ion milling were observed in Bi₂Sr₂CaCu₂O_8+y single-crystal films with antidot arrays as well as the thinning of the films. In an original sample with triangular array of antidots, whose diameter is about 200 nm, a few dip structures by the matching effect were observed in the vortex-flow resistance as a function of magnetic field. With increasing the milling time, the number of the dips increases and the appearance of the flow resistance becomes periodic oscillations. These features can be explained mainly by the increase of the antidot diameter.     

Generalizing Tutte’s theorem and maximal non-matchable graphs

A graph $G$ has a perfect matching if and only if $0$ is not a root of its matching polynomial $\mu (G,x)$. Thus, Tutte’s famous theorem asserts that $0$ is not a root of $\mu (G,x)$ if and only if $c_{\mathrm{odd}}(G?S)\le \left|S\right|$ for all $S?V\left(G\right)$, where $c_{\mathrm{odd}}\left(G\right)$ denotes the number of odd components of $G$. Tutte’s theorem can be proved using a characterization of the structure of maximal non-matchable graphs, that is, the edge-maximal graphs among those having no perfect matching. In this paper, we prove a generalized version of Tutte’s theorem in terms of avoiding any given real number $\theta$ as a root of $\mu (G,x)$. We also extend maximal non-matchable graphs to maximal $\theta$-non-matchable graphs and determine the structure of such graphs.     

Determination of acoustic impedances of multi matching layers for narrowband ultrasonic airborne transducers at frequencies <2.5 MHz - Application of a genetic algorithm

The effective ultrasonic energy radiation into the air of piezoelectric transducers requires using multilayer matching systems with accurately selected acoustic impedances and the thickness of particular layers. One major problem of ultrasonic transducers, radiating acoustic energy into air, is to find the proper acoustic impedances of one or more matching layers. This work aims at developing an original solution to the acoustic impedance mismatch between transducer and air. If the acoustic impedance defences between transducer and air be more, then finding best matching layer(s) is harder. Therefore we consider PZT (lead zirconate titanate piezo electric) transducer and air that has huge acoustic impedance deference. The vibration source energy (PZT), which is used to generate the incident wave, consumes a part of the mechanical energy and converts it to an electrical one in theoretical calculation. After calculating matching layers, we consider the energy source as layer to design a transducer. However, this part of the mechanical energy will be neglected during the mathematical work. This approximation is correct only if the transducer is open-circuit. Since the possibilities of choosing material with required acoustic impedance are limited (the counted values cannot always be realized and applied in practice) it is necessary to correct the differences between theoretical values and the possibilities of practical application of given acoustic impedances. Such a correction can be done by manipulating other parameters of matching layers (e.g. by changing their thickness). The efficiency of the energy transmission from the piezoceramic transducer through different layers with different thickness and different attenuation enabling a compensation of non-ideal real values by changing their thickness was computer analyzed (base on genetic algorithm). Firstly, three theoretical solutions were investigated. Namely, Chebyshev, Desilets and Souquet theories. However, the obtained acoustic impedances do not necessarily correspond to a nowadays available material. Consequently, the values of the acoustic impedances are switched to the nearest values in a large material database. The switched values of the acoustic impedances do not generally give efficient transmission coefficients. Therefore, we proposed, in a second step, the use of a genetic algorithm (GA) to select the best acoustic impedances for matching layers from the material database for a narrow band ultrasonic transducer that work at frequency below the 2.5 MHz by considering attenuation. However this bank is rich, the results get better. So the accuracy of the propose method increase by using a lot of materials with exact data for acoustic impedance and their attenuation, especially in high frequency. This yields highly more efficient transmission coefficient. In fact by using increasing number of layer we can increase our chance to find the best sets of materials with valuable both in acoustic impedance and low attenuation. Precisely, the transmission coefficient is almost equal to unity for the all studied cases. Finally the effect of thickness on transmission coefficient is investigated for different layers. The results showed that the transmission coefficient for air media is a function of thickness and sensitive to it even for small variation in thickness. In fact, the sensitivity increases when the differences of acoustic impedances to be high (difference between PZT and air).     

Large spaces of symmetric matrices of bounded rank are decomposable

Let k and n be positive integers such that k≤n. Let S_n(F) denote the space of all n×n symmetric matrices over the field F with char F≠2. A subspace L of S_n(F) is said to be a k-subspace if rank A≤k for every AεL.

Now suppose that k is even, and write k=2r. We say a k∥-subspace of S_n(F) is decomposable if there exists in Fⁿ a subspace W of dimension n-r such that x^tAx=0 for every xεWAεL.

We show here, under some mild assumptions on kn and F, that every k∥-subspace of S_n(F) of sufficiently large dimension must be decomposable. This is an analogue of a result obtained by Atkinson and Lloyd for corresponding subspaces of F^m,n.     

基于无人机红外光谱技术的影像数据匹配方法研究

无人机加载红外光谱载荷对区域内影像进行获取现已成为遥感领域一种重要的技术手段,可通过对携带位置信息的影像进行分类提取,得到植被盖度、温度指数等一系列因子指标。利用FREE BIRD(自由鸟)小型低空无人机系统挂载Tetracam红外相机(310万像素)对新疆玛纳斯县一河道进行影像获取。无人机飞行面积约为20.5 km2,为了得到更加精确的植被、温度等因子,需要对无人机红外影像进行配准,通过优化SIFT匹配参数和RANSAC粗差剔除后,获取了可靠的匹配结果,即经过算法匹配后的影像与原影像进行了误差比对,能够满足后期的应用需要, 这也是本文的创新点之一。将影像进行配准后进行二维影像拼接,将多张红外影像按照航向重叠度不低于60%,旁向重叠度不低于50%的概率进行拼接,得到拼接后的红外影像图。另外比较了SIFT和SUFT两种算法,利用优化的SIFT算法及改进的FLIR传感器获取1 600张热红外影像,利用地面同步测量数据对拼接后的红外影像进行算法匹配,并利用ENVI(完整的遥感图像处理平台)软件进行温度及植被盖度的影像反演,得到了研究区域的单一影像及红外影像的温度反演图及植被反演图。通过对两种算法的对比得到更加优化的算法模型,并对该模型进行回归分析和精度检验,得到该模型的相关系数R2为0.767,匹配精度为81.51%,模型精度较高。本模型的建立对日后无人机红外影像的配准及提取反演奠定了理论和实践基础。