Finding long and similar parts of trajectories

A natural time-dependent similarity measure for two trajectories is their average distance at corresponding times. We give algorithms for computing the most similar subtrajectories under this measure, assuming the two trajectories are given as two polygonal, possibly self-intersecting lines with time stamps. For the case when a minimum duration of the subtrajectories is specified and the subtrajectories must start at corresponding times, we give a linear-time algorithm. The algorithm is based on a result of independent interest: We present a linear-time algorithm to find, for a piece-wise monotone function, an interval of at least a given length that has minimum average value. In the case that the subtrajectories may start at non-corresponding times, it appears difficult to give exact algorithms, even if the duration of the subtrajectories is fixed. For this case, we give (1+ε)-approximation algorithms, for both fixed duration and when only a minimum duration is specified.     

On Local Integrability Conditions of Jet Groupoids

A jet groupoid ℛ _q over a manifold X is a special Lie groupoid consisting of q-jets of local diffeomorphisms X→X. As a subbundle of J ^q (X,X), a jet groupoid can be considered as a system of nonlinear partial differential equations (PDE). This leads to the question if ℛ _q is formally integrable. On the other hand, each jet groupoid is the symmetry groupoid of a geometric object, which is a section ω of a natural bundle ℱ. Using the jet groupoids, we give a local characterisation of formal integrability for transitive jet groupoids in terms of their corresponding geometric objects. Thanks to M. Barakat and W. Plesken for discussions. The author was supported by DFG Grant Graduiertenkolleg 775.     

On the Jordan–Hölder property for geometric derived categories

We prove that the semiorthogonal decompositions of the derived category of the classical Godeaux surface X   do not satisfy the Jordan–Hölder property. More precisely, there are two maximal exceptional sequences in this category, one of length 11, the other of length 9. Assuming the Noetherian property for semiorthogonal decompositions, one can define, following Kuznetsov, the Clemens–Griffiths component CG(D)$\mathrm{CG}(\mathfrak{D})$ for each fixed maximal decomposition D$\mathfrak{D}$. We then show that D^b(X)${\mathrm{D}}^b(X)$ has two different maximal decompositions for which the Clemens–Griffiths components differ. Moreover, we produce examples of rational fourfolds whose derived categories also violate the Jordan–Hölder property.     

基于遗传算法和满意度函数的武器系统维修性分配规划问题研究

武器系统维修性分配是一个复杂的多目标规划问题.常规求解方法得到的结果难以满足其约束条件,并且难以体现不同目标间重要性的差别.据此,通过引入遗传算法(GA)和满意度函数解决了上述问题.首先利用GA求解单目标的最优解,建立各目标的满意度函数并综合为一个总满意度函数,最后利用GA求总满意度的最大值,即可获得模型的满意解.仿真算例表明,GA算法可适用于解决武器系统维修性分配问题,同时多目标规划中采用满意度函数法比线性加权法更可行.     

Covering moving points with anchored disks

Consider a set of mobile clients represented by n points in the plane moving at constant speed along n different straight lines. We study the problem of covering all mobile clients using a set of k disks centered at k fixed centers. Each disk exists only at one instant and while it does, covers any client within its coverage radius. The task is to select an activation time and a radius for each disk such that every mobile client is covered by at least one disk. In particular, we study the optimization problem of minimizing the maximum coverage radius. First we prove that, although the static version of the problem is polynomial, the kinetic version is NP-hard. Moreover, we show that the problem is not approximable by a constant factor (unless P = NP). We then present a generic framework to solve it for fixed values of k, which in turn allows us to solve more general optimization problems. Our algorithms are efficient for constant values of k.     

基于有限穿越可视图的时间序列网络模型

提出了一种改进的时间序列有限穿越可视图建网方法,并对三种可视图(可视图、水平可视图、有限穿越可视图)网络度分布进行了评价.结果表明:水平可视图网络均无法有效识别各类时间序列信号(周期、分形、混沌);对分形信号,可视图及有限穿越可视图网络均具有无标度幂律形式,但抗噪能力较差;对周期信号及混沌信号,有限穿越可视图网络比可视图具有更强的抗噪性.在此基础上,采用有限穿越可视图网络从油气水三相流电导波动信号中提取了度分布特征参数,通过其特征参数组合实现了对三种典型三相流流型(水包油泡状流、水包油泡状-段塞过渡流型及水包油段塞流)较好的辨识效果.     

Inverse scattering by an inhomogeneous penetrable obstacle in a piecewise homogeneous medium

This paper is concerned with the inverse problem of scattering of time-harmonic acoustic waves by an inhomogeneous penetrable obstacle in a piecewise homogeneous medium. The well-posedness of the direct problem is first established by using the integral equation method. We then proceed to establish two tools that play important roles for the inverse problem: one is a mixed reciprocity relation and the other is a priori estimates of the solution on some part of the interfaces between the layered media. For the inverse problem, we prove in this paper that both the penetrable interfaces and the possible inside inhomogeneity can be uniquely determined from a knowledge of the far field pattern for incident plane waves.     

Fixed period of temporary immunity after run of anti-malicious software on computer nodes

SIRS epidemic model has been developed with a fixed period of temporary immunity, following temporary recovery from the infection of malicious objects in place of an exponentially distributed period of temporary immunity. When a node is recovered from the infected class, it recovers temporarily, acquiring temporary immunity with probability p (0  p  1) and dies from the attack of malicious object with probability (1 − p). Temporary immunity is observed in the computer network when anti-malicious software is run after a node gets affected by a malicious object(s). The model consists of a set of integro-differential equations. The stability of the results is stated in terms of threshold parameter. It has been observed that the endemic equilibrium for this model may be unstable thus giving an example of a generalization which leads to new possibilities for the behavior of the model. Numerically it has been verified that the endemic equilibrium is not asymptotically stable for all parameter values.     

Research on Antenna Temperature Contrast of Metal Solid Objects

It is necessary to study the radiation characteristic of metal solid objects for millimeter wave passive guidance. On basis of discussing the grounded theory, the antenna temperature contrast formula of metal solid objects is presented. Furthermore equivalent radiometric section coefficient based on scale-shrinking measuring theory is proposed in favor of engineering applications. The data error between 8mm theoretical calculation and actual measurement are mostly below 1K. So equivalent radiometric section coefficient gives a virtual way for engineering calculation and measurement of metal solid objects.     

Contrast increasing by third-order nonlinear image processing: a numerical study for microscopic rectangular objects

This study deals with the simulation of the image formation involved by using a nonlinear image processor composed of a nonlinear medium placed at the common focus of a 4-f system. A simple linear model is developed taking into account the third-order optical nonlinearity of the medium (in the general case of nonlinear absorption and dephasing) and the optical transfer function of the 4-f system. The simulated images through the system are given for phase and/or amplitude rectangular objects. Our model and its corresponding simulation lead to optimizing nonlinear parameters of the medium for this class of objects, whatever their transmittance is, in order to enhance the visibility in image processors.