Estimating montane forest above-ground biomass in the upper reaches of the Heihe River Basin using Landsat-TM data

In this work, the results of above-ground biomass (AGB) estimates from Landsat Thematic Mapper 5 (TM) images and field data from the fragmented landscape of the upper reaches of the Heihe River Basin (HRB), located in the Qilian Mountains of Gansu province in northwest China, are presented. Estimates of AGB are relevant for sustainable forest management, monitoring global change, and carbon accounting. This is particularly true for the Qilian Mountains, which are a water resource protection zone. We combined forest inventory data from 133 plots with TM images and Advanced Spaceborne Thermal Emission and Reflection Radiometer (ASTER) global digital elevation model (GDEM) V2 products (GDEM) in order to analyse the influence of the sun-canopy-sensor plus C (SCS+C) topographic correction on estimations of forest AGB using the stepwise multiple linear regression (SMLR) and k-nearest neighbour (k-NN) methods. For both methods, our results indicated that the SCS+C correction was necessary for getting more reliable forest AGB estimates within this complex terrain. Remotely sensed AGB estimates were validated against forest inventory data using the leave-one-out (LOO) method. An optimized k-NN method was designed by varying both mathematical formulation of the algorithm and remote-sensing data input, which resulted in 3000 different model configurations. Following topographic correction, performance of the optimized k-NN method was compared to that of the regression method. The optimized k-NN method (R² = 0.59, root mean square error (RMSE) = 24.92 tonnes ha^–1) was found to perform much better than the regression method (R² = 0.42, RMSE = 29.74 tonnes ha^–1) for forest AGB retrieval over this montane area. Our results indicated that the optimized k-NN method is capable of operational application to forest AGB estimates in regions where few inventory data are available.     

The SOR-k method for linear systems with p-cyclic matrices

Let the system matrix of a linear system be p-cyclic and consistently ordered. Under the assumption that the pth power of the associated Jacobi matrix has only non-positive eigenvalues, it is known that the optimal spectral radius of the SOR-k iteration matrix is strictly increasing as k increases from 2 to p. In this paper, we first show that the optimal parameter of the SOR-k method as a function of k is strictly increasing. The behaviour of the spectral radius of the SOR-k method (for fixed parameter) is then studied.     

On problems without polynomial kernels

Kernelization is a strong and widely-applied technique in parameterized complexity. A kernelization algorithm, or simply a kernel, is a polynomial-time transformation that transforms any given parameterized instance to an equivalent instance of the same problem, with size and parameter bounded by a function of the parameter in the input. A kernel is polynomial if the size and parameter of the output are polynomially-bounded by the parameter of the input.In this paper we develop a framework which allows showing that a wide range of FPT problems do not have polynomial kernels. Our evidence relies on hypothesis made in the classical world (i.e. non-parametric complexity), and revolves around a new type of algorithm for classical decision problems, called a distillation algorithm, which is of independent interest. Using the notion of distillation algorithms, we develop a generic lower-bound engine that allows us to show that a variety of FPT problems, fulfilling certain criteria, cannot have polynomial kernels unless the polynomial hierarchy collapses. These problems include k-Path, k-Cycle, k-Exact Cycle, k-Short Cheap Tour, k-Graph Minor Order Test, k-Cutwidth, k-Search Number, k-Pathwidth, k-Treewidth, k-Branchwidth, and several optimization problems parameterized by treewidth and other structural parameters.     

Histogram matching for the calibration of kNN stem volume estimates

The k-nearest neighbours (kNN) methods have been used successfully in many countries for the production of spatially comprehensive raster databases of forest attributes, made from the combination of National Forest Inventory (NFI) and satellite data. In Sweden, country-wide kNN estimates of forest variables have been produced to represent the forest condition in the years 2000 and 2005 by using a combination of Système Pour l'Observation de la Terre 5 (SPOT 5) satellite data and field data from the Swedish NFI. The resulting products are wall-to-wall raster maps with estimates of total stem volume, stem volume per tree species, tree height and stand age and a 25?×?25 m² pixel resolution. However, probability-based kNN stem volume estimates tend to have a suppressed variation range as large values are usually underestimated and small values are overestimated. One way to handle this problem is to calibrate the kNN stem volume estimates to the reference distribution of stem volume observations by histogram matching (HM) for a defined geographic area.

In this study, we have tested HM for the calibration of kNN total stem volume raster maps to the reference distribution captured by a forest inventory (FI) from 106 stands in Strömsjöliden, in the north of Sweden. The available field FI data set comprises 1084 circular plots, divided into a reference data set and an evaluation data set of total stem volume observations. The reference data set was used for the creation of a cumulative frequency histogram of total stem volume and the evaluation data set was used to assess the accuracy of volume estimates, before and after HM. The HM adjusted the cumulative distribution of the kNN data set to the distribution of the reference observations and resulted in a distribution of kNN estimates of total stem volume, which corresponded closely to that of the evaluation data set. The results show that the variation range of the kNN stem volume estimates can be extended by HM both on the pixel and stand levels. The extension of the range of estimates towards the range provided by the field observations allows improvement of kNN volume estimation for use in forest management planning based on stand-level analysis, given that the reference stem volume distribution can be estimated accurately, for example, using field data from NFI.     

Nodal Superconvergence of SDFEM for Singularly Perturbed Problems

In this paper, we analyze the streamline diffusion finite element method for one dimensional singularly perturbed convection-diffusion-reaction problems. Local error estimates on a subdomain where the solution is smooth are established. We prove that for a special group of exact solutions, the nodal error converges at a superconvergence rate of order (ln ε ⁻¹/N)^2k (or (ln N/N)^2k ) on a Shishkin mesh. Here ε is the singular perturbation parameter and 2N denotes the number of mesh elements. Numerical results illustrating the sharpness of our theoretical findings are displayed.     

PI‐PD controller design for time delay systems via the weighted geometrical center method

In this study, a PI‐PD controller tuning method is presented using the weighted geometrical center method, which is based on the calculation of the weighted geometric center of the stability region obtained by the stability boundary locus method. The proposed method for tuning of PI‐PD controller parameters (k_d,k_f,k_p and k_i ) is performed in three steps. In the first step, the (k_d,k_f) parameter region for the inner loop with PD controller is obtained, and then the weighted geometric center of this region is calculated. In the second step, the inner PD loop is reduced to a single block using the numerical values of (k_d,k_f) that are obtained in the first step. Then, the (k_p,k_i) values of the external loop with PI controller are determined by the same procedure. This tuning method has some advantages over other tuning methods in terms of simplicity and robustness. The simulation examples show that a PI‐PD controller designed using the proposed method provides good performance results when compared to other tuning methods presented in the literature.     

Modelling and solving the intrusion detection problem in computer networks

We introduce a novel anomaly intrusion detection method based on a Within-Class Dissimilarity, WCD. This approach functions by using an appropriate metric WCD to measure the distance between an unknown user and a known user defined respectively by their profile vectors. First of all, each user performs a set of commands (events) on a given system (Unix for example). The events vector of a given user profile is a binary vector, such that an element of this vector is equal to “1” if an event happens, and to “0” otherwise. In addition to this, each user's class k has a typical profile defined by the vector P_k, in order to test if a new user i defined by its profile vector P_i belongs to the same class k or not. The P_k vector is a weighted events vector E_k, such that each weight represents the number of occurrences of an event e_k. If the “distance” d_ki (measured by a dissimilarity parameter) between an unknown profile P_i and a known profile P_k is reasonable according to a given threshold and to some constraints, then there is no intrusion. Else, the user i is suspicious. A simple example illustrates the WCD procedure. A survey of intrusion detection methods is presented.Our proposed method based on clustering users and using simple statistical formulas is very easy for implementation.     

L ∞-error estimates of higher order mixed finite element approximations for elliptic optimal control problems

In this paper, we investigate the L ^∞-error estimates of the numerical solutions of linear-quadratic elliptic control problems by using higher order mixed finite element methods. The state and co-state are approximated by the order k Raviart-Thomas mixed finite element spaces and the control variable is approximated by piecewise polynomials of order k (k≥1). Optimal L ^∞-error estimates are derived for both the control and the state approximations. These results are seemed to be new in the literature of the mixed finite element methods for optimal control problems.     

取定s的严格d-正则随机(3,2s)-SAT问题的可满足临界

3-CNF公式的随机难解实例生成对于揭示3-SAT问题的难解实质和设计满足性测试的有效算法有着重要意义.对于整数k>2和s>0,如果在一个k-CNF公式中每个变量正负出现次数均为s,则称该公式是严格正则（k,2s）-CNF公式.受严格正则（k,2s）-CNF公式的结构特征启发,提出每个变量正负出现次数之差的绝对值均为d的严格d-正则（k,2s）-CNF公式,并使用新提出的SDRRK2S模型生成严格d-正则随机（k,2s）-CNF公式.取定整数5<s<11,模拟实验显示,严格d-正则随机（3,2s）-SAT问题存在SAT-UNSAT相变现象和HARD-EASY相变现象.因此,立足于3-CNF公式的随机难解实例生成,研究了严格d-正则随机（3,2s）-SAT问题在s取定时的可满足临界.通过构造一个特殊随机实验和使用一阶矩方法,得到了严格d-正则随机（3,2s）-SAT问题在s取定时可满足临界值的一个下界.模拟实验结果验证了理论证明所得下界的正确性.     

Suburban atmospheric visibility sensing by an image degradation processor: model development and field test

This study describes some preliminary results of a new approach which seeks to develop a method by which uneven decay of atmosphere can be described by the fluctuation of a degradation parameter, k, extracted from online recorded images. The proposed processor is a combination of the empirical model for atmospheric non-homogeneity and an image degradation method. Estimation of the other parameter, C _ave, derived from k values was an attempt to quantify the blurred level of atmospheric visibility according to the full-scale image computation. The C _ave of code A–E images ranged from 0.437 to 0.831, and the related visual range observed by investigators was from 14.1 to 3.0 km, respectively. The standard deviation of C _ave reveals that non-homogeneous degradation of blurring atmosphere happens. Low visibility related with a small visual range and a degraded image is companied by a large C _ave and inherits high variation from heaving k values. Because of fluctuation and full-scale image representation, C _ave is more meaningful and sensitive for atmospheric decay measurement than the prevailing visibility equal to the distance at which the farthest target can be recognized. Finally, a field test was applied to confirm a good correlation between observed visual range and two parameters (k and C _ave).     

Consensus seeking in a network of discrete-time linear agents with communication noises

This paper studies the mean square consensus of discrete-time linear time-invariant multi-agent systems with communication noises. A distributed consensus protocol, which is composed of the agent's own state feedback and the relative states between the agent and its neighbours, is proposed. A time-varying consensus gain a[k] is applied to attenuate the effect of noises which inherits in the inaccurate measurement of relative states with neighbours. A polynomial, namely ‘parameter polynomial’, is constructed. And its coefficients are the parameters in the feedback gain vector of the proposed protocol. It turns out that the parameter polynomial plays an important role in guaranteeing the consensus of linear multi-agent systems. By the proposed protocol, necessary and sufficient conditions for mean square consensus are presented under different topology conditions: (1) if the communication topology graph has a spanning tree and every node in the graph has at least one parent node, then the mean square consensus can be achieved if and only if ∑^∞_{k = 0}a[k] = ∞, ∑^∞_{k = 0}a²[k] < ∞ and all roots of the parameter polynomial are in the unit circle; (2) if the communication topology graph has a spanning tree and there exits one node without any parent node (the leader–follower case), then the mean square consensus can be achieved if and only if ∑^∞_{k = 0}a[k] = ∞, lim_{k → ∞}a[k] = 0 and all roots of the parameter polynomial are in the unit circle; (3) if the communication topology graph does not have a spanning tree, then the mean square consensus can never be achieved. Finally, one simulation example on the multiple aircrafts system is provided to validate the theoretical analysis.     

A multiple-point spatially weighted k-NN classifier for remote sensing

A novel classification method based on multiple-point statistics (MPS) is proposed in this article. The method is a modified version of the spatially weighted k-nearest neighbour (k-NN) classifier, which accounts for spatial correlation through weights applied to neighbouring pixels. The MPS characterizes the spatial correlation between multiple points of land-cover classes by learning local patterns in a training image. This rich spatial information is then converted to multiple-point probabilities and incorporated into the k-NN classifier. Experiments were conducted in two study areas, in which the proposed method for classification was tested on a WorldView-2 sub-scene of the Sichuan mountainous area and an IKONOS image of the Beijing urban area. The multiple-point weighted k-NN method (MPk-NN) was compared to several alternatives; including the traditional k-NN and two previously published spatially weighted k-NN schemes; the inverse distance weighted k-NN, and the geostatistically weighted k-NN. The classifiers using the Bayesian and Support Vector Machine (SVM) methods, and these classifiers weighted with spatial context using the Markov random field (MRF) model, were also introduced to provide a benchmark comparison with the MPk-NN method. The proposed approach increased classification accuracy significantly relative to the alternatives, and it is, thus, recommended for the identification of land-cover types with complex and diverse spatial distributions.     

Optimal Error Estimates of the Local Discontinuous Galerkin Method for Surface Diffusion of Graphs on Cartesian Meshes

In (Xu and Shu in J. Sci. Comput. 40:375–390, 2009), a local discontinuous Galerkin (LDG) method for the surface diffusion of graphs was developed and a rigorous proof for its energy stability was given. Numerical simulation results showed the optimal order of accuracy. In this subsequent paper, we concentrate on analyzing a priori error estimates of the LDG method for the surface diffusion of graphs. The main achievement is the derivation of the optimal convergence rate k+1 in the L ² norm in one-dimension as well as in multi-dimensions for Cartesian meshes using a completely discontinuous piecewise polynomial space with degree k≥1.     

Nearest-neighbor classifier motivated marginal discriminant projections for face recognition

Marginal Fisher analysis (MFA) is a representative margin-based learning algorithm for face recognition. A major problem in MFA is how to select appropriate parameters, k ₁ and k ₂, to construct the respective intrinsic and penalty graphs. In this paper, we propose a novel method called nearest-neighbor (NN) classifier motivated marginal discriminant projections (NN-MDP). Motivated by the NN classifier, NN-MDP seeks a few projection vectors to prevent data samples from being wrongly categorized. Like MFA, NN-MDP can characterize the compactness and separability of samples simultaneously. Moreover, in contrast to MFA, NN-MDP can actively construct the intrinsic graph and penalty graph without unknown parameters. Experimental results on the ORL, Yale, and FERET face databases show that NN-MDP not only avoids the intractability, and high expense of neighborhood parameter selection, but is also more applicable to face recognition with NN classifier than other methods.     

Finite-time settling adaptive observer for linear discrete-time systems

This paper deals with a design method for an adaptive scheme which would identify the parameters and observe the state of any unknown single-input single-output linear discrete-time systems using only input-output data. Kreisselmeier's parametrized system [5] is used instead of the original system. Then the parameter identification process and the state observation process are well separated. To accelerate the convergence rate of the estimates, a finite-time settling scheme is proposed. It is shown that the estimates obtained converges to true values at k = 3n ?1, where k is the discrete time and n is the order of system. A numerical example is given to indicate acceptable performance of the proposed scheme.     

Application of a fast simulation method to the estimation of the number of some <Emphasis Type="Italic">k</Emphasis>-dimensional subspaces over a finite space

A fast simulation method is proposed for estimation of the number of k-dimensional subspaces of weight w in an n-dimensional vector space over the Galois field containing q components. Unbiased estimates are constructed for the cases when w = 1 and w = 2, and lower and upper estimates are proposed for the case when w = 3. It is proved that the relative error remains bounded as q → ∞. A high accuracy of the method proposed is illustrated by numerical examples.     

Adaptive soft k-nearest-neighbour classifiers

A novel classifier is introduced to overcome the limitations of the k-NN classification systems. It estimates the posterior class probabilities using a local Parzen window estimation with the k-nearest-neighbour prototypes (in the Euclidean sense) to the pattern to classify. A learning algorithm is also presented to reduce the number of data points to store. Experimental results in two hand-written classification problems demonstrate the potential of the proposed classification system.     

A Dynamic k-Nearest Neighbor Method for WLAN-Based Positioning Systems

The static k-Nearest Neighbor (k-NN) method for localization has limitations in accuracy due to the fixed k value in the algorithm. To address this problem, and achieve better accuracy, we propose a new dynamic k-Nearest Neighbor (Dk-NN) method in which the optimal k value changes based on the topologies and distances of its nearest neighbors. The proposed method has been validated using the WLAN-fingerprint data sets collected at COEX, one of the largest convention centers in Seoul, Korea. The proposed method significantly reduced both the mean error distances and the standard deviations of location estimations, leading to a significant improvement in accuracy by ~ 23% compared to the cluster filtered k-NN (CFK) method, and ~ 17% compared to the k-NN (k = 1) method.     

Kernels for feedback arc set in tournaments

A tournament T=(V,A) is a directed graph in which there is exactly one arc between every pair of distinct vertices. Given a digraph on n vertices and an integer parameter k, the Feedback Arc Set problem asks whether the given digraph has a set of k arcs whose removal results in an acyclic digraph. The Feedback Arc Set problem restricted to tournaments is known as the k-Feedback Arc Set in Tournaments (k-FAST) problem. In this paper we obtain a linear vertex kernel for k-FAST. That is, we give a polynomial time algorithm which given an input instance T to k-FAST obtains an equivalent instance T^′ on O(k) vertices. In fact, given any fixed ?>0, the kernelized instance has at most (2+?)k vertices. Our result improves the previous known bound of O(k²) on the kernel size for k-FAST. Our kernelization algorithm solves the problem on a subclass of tournaments in polynomial time and uses a known polynomial time approximation scheme for k-FAST.