Kernel Elements Research Articles

Verification of realizability of boolean functions by a neural element with a threshold activation function

A widespread application of neural network circuits from neural elements with a threshold activation function would be possible if efficient methods for the verification of realizability of functions of the algebra of logic by one neural element are devised, as well as the synthesis of these elements with a large number of inputs. The article examines algebraic structure of kernels and reduced kernels of Boolean functions. A connection is established between the kernels of Boolean functions that are implemented by one neural element with a threshold activation function and tolerance matrices. Based on the convex linear combination of kernel elements of functions of the algebra of logic, we proved a criteria of their realizability by one neural element with a threshold activation function. By using algebraic properties of kernels in Boolean functions and the representations of their reduced kernels by tolerance matrices, we obtained a number of easily verified necessary conditions for the realizability of functions of the algebra of logic by one neural element. These necessary conditions in many cases make it possible not to perform complicated calculations by the methods of approximation of different orders and by the iterative methods, in which, by means of limit cycles, the realizability or non-realizability of Boolean functions by one neural element with a threshold activation function is determined. Based on the sufficient conditions, obtained in the work, for the realizability of functions of the algebra of logic by one neural element, we devised an effective method for the synthesis of integer neural elements with a large number of inputs.

Innovation of Bilingual Teaching in Packaging Engineering at Institution of Higher Learning Based upon Requirement of Quality Improvement and Connotative Development

On the basis of comprehensively surveying the background and current situation of bilingual teaching implementation at institutions of higher learning, China, the distinct difference between bilingual courses and academic English for packaging in terms of bilingually educational model is clearly defined. It is emphasized that bilingual teaching in packaging engineering should protrude such kernel elements as packaging knowledge, and heighten the level of students who are able to apply foreign languages to carry on communications in discipline and specialty. In the meanwhile, the implementation of bilingual teaching ought to first and foremost be sustained, and how to foster the packaging professionals with international horizon and competitiveness is dwelled on. Ultimately, it is recommended that the innovative bilingual teaching model should be explored to accommodate the colleges and specialties concerned, inclusive of these key factors like teaching team, curriculum, teaching contents and resources, teaching means and methods, and the acceleration of the pace of course construction is taken as an important starting point and the connotative development of bilingual teaching is really implemented to elevate the quality of bilingual teaching in packaging engineering through deepening innovation of bilingual teaching.

Shape-memory alloys as macrostrain sensors

The present paper studies the feasibility, through physical experimentation, of efficient and low-cost macrostrain sensors, based on shape-memory alloy technologies. The motivation of this work is to explore the intrinsic relation between electrical resistivity and strain, associated with the development of the stress induced martensitic transformation in superelastic shape-memory alloys. This property enables the material to endure deformations up to 8% without any residual strains, making shape-memory alloy wires excellent candidates for kernel elements in innovative strain transducers with dynamic ranges 4 to 5 times larger than the currently available strain transducers. An experimental prototype of a beam with a set of SMA macrostrain sensors is presented, featuring a timed scanning sequential algorithm to successfully perform the resistance readings. The aim of this work is to provide an additional insight into the potential of SMAs in new macrostrain measurement applications. Copyright © 2016 John Wiley & Sons, Ltd.

The Role of PREMIS Preservation Metadata in Information Management in Virtual Museums

Through application of novel information technologies, virtual museums try to deliver the data to their users in any form and at any time that this requires information and resource management. Therefore, the use of metadata that is in accordance with novel technologies is necessary in main virtual environments. Each of the metadata has distinct responsibilities and can cooperate and have complementary roles along with others and through expressing museum objects characteristic, metadata describes them in a systematic way. The standard PREMIS preservation metadata maintenance schema, which is based on XML, has been developed in order to record metadata related to maintaining information resource in digital packages. In other words, this metadata provides the possibility of self documentation for digital data. This standard schema suggests an aggregate of kernel and application metadata elements. Every digital package should be aware of this aggregate in order to preserve its resources in long-term. Findings indicate that PREMIS preservation metadata has a determining role in optimal information management in virtual museums.

K-space reconstruction with anisotropic kernel support (KARAOKE) for ultrafast partially parallel imaging.

Partially parallel imaging (PPI) greatly accelerates MR imaging by using surface coil arrays and under-sampling k-space. However, the reduction factor (R) in PPI is theoretically constrained by the number of coils (N(C)). A symmetrically shaped kernel is typically used, but this often prevents even the theoretically possible R from being achieved. Here, the authors propose a kernel design method to accelerate PPI faster than R = N(C). K-space data demonstrates an anisotropic pattern that is correlated with the object itself and to the asymmetry of the coil sensitivity profile, which is caused by coil placement and B(1) inhomogeneity. From spatial analysis theory, reconstruction of such pattern is best achieved by a signal-dependent anisotropic shape kernel. As a result, the authors propose the use of asymmetric kernels to improve k-space reconstruction. The authors fit a bivariate Gaussian function to the local signal magnitude of each coil, then threshold this function to extract the kernel elements. A perceptual difference model (Case-PDM) was employed to quantitatively evaluate image quality. A MR phantom experiment showed that k-space anisotropy increased as a function of magnetic field strength. The authors tested a K-spAce Reconstruction with AnisOtropic KErnel support ("KARAOKE") algorithm with both MR phantom and in vivo data sets, and compared the reconstructions to those produced by GRAPPA, a popular PPI reconstruction method. By exploiting k-space anisotropy, KARAOKE was able to better preserve edges, which is particularly useful for cardiac imaging and motion correction, while GRAPPA failed at a high R near or exceeding N(C). KARAOKE performed comparably to GRAPPA at low Rs. As a rule of thumb, KARAOKE reconstruction should always be used for higher quality k-space reconstruction, particularly when PPI data is acquired at high Rs and/or high field strength.

Mesh filtering algorithm using an adaptive 3D convolution kernel applied to a volume-based vector distance field

This paper addresses the problem of feature preserving mesh filtering, which occurs in surface reconstruction of scanned objects, which include acquisition noise to be removed without altering sharp edges. We propose a method based on a vector field distance transform of the mesh to process. It is a volume-based implicit surface modeling, which provides an alternative representation of meshes. We use an adaptive 3D convolution kernel applied to the voxels of the distance transform model. Weights of the kernel elements are determined according to the angle between the vectors of the implicit field. We also propose a new adaptation of the Marching Cubes algorithm in order to extract the isosurface from the vector implicit field after the filtering process. We compare our method to the previous one introduced using the vector field representation and to other feature preserving adaptive filtering algorithms. According to error metric evaluations, we show that our new design provides high quality filtering results while better preserving geometric features.

Langevin agglomeration of nanoparticles interacting via a central potential

Nanoparticle agglomeration in a quiescent fluid is simulated by solving the Langevin equations of motion of a set of interacting monomers in the continuum regime. Monomers interact via a radial rapidly decaying intermonomer potential. The morphology of generated clusters is analyzed through their fractal dimension df and the cluster coordination number. The time evolution of the cluster fractal dimension is linked to the dynamics of two populations: small (k≤ 15) and large (k>15) clusters. At early times monomer-cluster agglomeration is the dominant agglomeration mechanism (d(f)=2.25) , whereas at late times cluster-cluster agglomeration dominates (d(f)=1.56). Clusters are found to be compact (mean coordination number of ∼5), tubular, and elongated. The local compact structure of the aggregates is attributed to the isotropy of the interaction potential, which allows rearrangement of bonded monomers, whereas the large-scale tubular structure is attributed to its relatively short attractive range. The cluster translational diffusion coefficient is determined to be inversely proportional to the cluster mass and the (per-unit-mass) friction coefficient of an isolated monomer, a consequence of the neglect of monomer shielding in a cluster. Clusters generated by unshielded Langevin equations are referred to as ideal clusters because the surface area accessible to the underlying fluid is found to be the sum of the accessible surface areas of the isolated monomers. Similarly, ideal clusters do not have, on average, a preferential orientation. The decrease in the numbers of clusters with time and a few collision kernel elements are evaluated and compared to analytical expressions.

Explaining the immobility of conjuncts*

Abstract. This paper aims to explain the well‐observed constraint that no conjunct may move. It is claimed that, with respect to final conjuncts, this constraint simply manifests a morphological property of coordinators shared with many other types of head elements: they need to be adjacent to their complement, and thus neither deletion nor movement of their complement is possible. Final conjuncts therefore may not move. Based on the assumption that the categorial features of initial conjuncts are transferred to the coordinator and, it is claimed that this transference keeps initial conjuncts in situ, since elements without category‐features may not move overtly. This new account for the immobility of initial conjuncts is supported by two generalizations. Firstly, in the Chinese de construction, kernel elements may not move because they provide categorial features for de, which has no intrinsic categorial features and is the head of the whole complex. Secondly, in the comitative coordinate construction in Chinese, initial conjuncts may move because they do not provide categorial features for the coordinators, which have their own intrinsic categorial features. This paper specifies the semantic condition of initial conjunct movement: the coordination must be non‐distributive. This new account of the immobility of conjuncts suggests that the constraint is not a construction‐specific syntactic constraint. Instead, it is related to the lexical/morphological makeup of coordinators. Conjuncts as regular Spec and Complement elements may undergo syntactic movement. It has been generally assumed that movement is driven by morphological considerations. This study further shows that the blocking of movement can also be related to morphological properties of specific syntactic elements in addition to the generally recognized locality restrictions.

Theoretical Foundations of Spatially-Variant Mathematical Morphology Part II: Gray-Level Images

In this paper, we develop a spatially-variant (SV) mathematical morphology theory for gray-level signals and images in the Euclidean space. The proposed theory preserves the geometrical concept of the structuring function, which provides the foundation of classical morphology and is essential in signal and image processing applications. We define the basic SV gray-level morphological operators (i.e., SV gray-level erosion, dilation, opening, and closing) and investigate their properties. We demonstrate the ubiquity of SV gray-level morphological systems by deriving a kernel representation for a large class of systems, called V-systems, in terms of the basic SV graylevel morphological operators. A V-system is defined to be a gray-level operator, which is invariant under gray-level (vertical) translations. Particular attention is focused on the class of SV flat gray-level operators. The kernel representation for increasing V-systems is a generalization of Maragos' kernel representation for increasing and translation-invariant function-processing systems. A representation of V-systems in terms of their kernel elements is established for increasing and upper-semi-continuous V-systems. This representation unifies a large class of spatially-variant linear and non-linear systems under the same mathematical framework. Finally, simulation results show the potential power of the general theory of gray-level spatially-variant mathematical morphology in several image analysis and computer vision applications.

ARM 9 임베디드 시스템에 의한 무선 컨텐츠 액세스 PMP 구현

본 논문에서는 무선 네트워크에 의하여 서버의 저장장치를 자체의 파일 시스템으로 연결하여 미디어 컨텐츠를 액세스하므로, HDD 등의 자체 대용량 저장 장치 없이 많은 양의 다양한 컨텐츠를 재생할 수 있는 PMP를 구현함을 다루었다. 이를 구현하기 위하여, 803.11x의 무선 LAN에 의한 NFS 프로토콜을 사용하여 원격의 파일을 PMP에 무선으로 접속하고, 문서, 정지영상, 동영상 등의 파일을 재생하고 저장하는 기능을 ARM9 계열의 PXA255 임베디드 프로세서 보드와, Linux 운영체제를 사용하여 구현하였다. 구현된 PMP를 다양한 멀티미디어 컨텐츠를 대상으로 실험하여 기능과 성능을 확인하였다. 이를 위하여 타겟 보드의 하드웨어 및 소프트웨어 구성요소에 따라 디바이스 드라이버를 선택하여 Linux 커널을 생성하여 타켓 보드에 실장하였다. 연구 결과로 목적한 기능과 성능을 확인 할 수 있었다.

Application of an inverse kernel concept to Monte Carlo based IMRT

Inverse treatment planning by means of pencil beam algorithms can lead to errors in the calculation of dose in areas without secondary electron equilibrium. Monte Carlo (MC) simulations give accurate results in such areas but result in increased computation times. We present a new, so-called inverse kernel concept that offers MC precision in inverse treatment planning with acceptable computation times and memory consumption. Inverse kernels are matrices that describe the dose contribution from all bixels of a beam to a distinct voxel of the patient phantom. The concept is similar to other generalized pencil-beam concepts, except that inverse kernel elements are precalculated using a single MC simulation and stored as binary trees. In this procedure a modified MC code (XVMC) is applied to trace the photon history for each dose deposition. Iterative optimization is then applied in a second step. The inverse process is separated into (i) a slower MC simulation and (ii) a faster iterative optimization, followed by (iii) the segmentation procedure, and (iv) a final MC dose calculation step including a segment weight reoptimization. Inverse kernel optimization, or IKO, with segmentation and reoptimization steps is demonstrated by means of a lung cancer case. To demonstrate the superiority of an inverse MC system over pencil-beam or collapsed-cone based systems, the final result of the IKO is compared to plans where all segments have been calculated by pencil beam or collapsed cone, respectively. Dose-volume histograms and dose-difference histograms show remarkable differences, which can be attributed to systematic errors in both algorithms. IKO is a precise, nonhybrid, inverse MC treatment planning system which suits current clinical needs, as several optimization steps can follow one single MC-simulation step for a distinct beam setup.

An algebraic multigrid method with interpolation reproducing rigid body modes for semi-definite problems in two-dimensional linear elasticity

Based on the geometric grid information as geometric coordinates, an algebraic multigrid (AMG) method with the interpolation reproducing the rigid body modes (namely the kernel elements of semi-definite operator arising from linear elasticity) is constructed, and such method is applied to the linear elasticity problems with a traction free boundary condition and crystal problems with free boundary conditions as well. The results of various numerical experiments in two dimensions are presented. It is shown from the numerical results that the constructed AMG method is robust and efficient for such semi-definite problems, and the convergence is uniformly bounded away from one independent of the problem size. Furthermore, the AMG method proposed in this paper has better convergence rate than the commonly used AMG methods. Simultaneously, an AMG method that can preserve the quotient space, which means that if the exact solution of original problem belongs to the quotient space of discrete operator considered, then the numerical solution of AMG method is convergent in the same quotient space, is obtained using the technique of orthogonal decomposition.

Advances in Lee–Schetzen Method for Volterra Filter Identification

This paper concerns the identification of nonlinear discrete causal systems that can be approximated with the Wiener--Volterra series. Some advances in the efficient use of Lee--Schetzen (L--S) method are presented, which make practical the estimate of long memory and high order models. Major problems in L--S method occur in the identification of diagonal kernel elements. Two approaches have been considered: approximation of gridded data, with interpolation or smoothing, and improved techniques for diagonal elements estimation. A comparison of diagonal elements estimated, with different methods has been shown with extended tests on fifth order Volterra systems.

Lattice Image Processing: A Unification of Morphological and Fuzzy Algebraic Systems

This paper explores some aspects of the algebraic theory of mathematical morphology from the viewpoints of minimax algebra and translation-invariant systems and extends them to a more general algebraic structure that includes generalized Minkowski operators and lattice fuzzy image operators. This algebraic structure is based on signal spaces that combine the sup-inf lattice structure with a scalar semi-ring arithmetic that possesses generalized ‘additions’ and ✶-‘multiplications’. A unified analysis is developed for: (i) representations of translation-invariant operators compatible with these generalized algebraic structures as nonlinear sup-✶ convolutions, and (ii) kernel representations of increasing translation-invariant operators as suprema of erosion-like nonlinear convolutions by kernel elements. The theoretical results of this paper develop foundations for unifying large classes of nonlinear translation-invariant image and signal processing systems of the max or min type. The envisioned applications lie in the broad intersection of mathematical morphology, minimax signal algebra and fuzzy logic.

An LP approach to compute the pre-kernel for cooperative games

We present an algorithm to compute the (pre)-kernel of a TU-game 〈 N , ν 〉 with a system of n 2 + 1 linear programming problems. In contrast to the algorithms using convergence methods to compute a point of the (pre)-kernel the emphasis of the chosen method lies not on efficiency and guessing good starting points but on computing large parts or in good cases the whole (pre)-kernel of a game. The chosen algorithm computes on a first step by relying on linear programming the n 2 largest bi-symmetrical amounts δ ij ε which can be transferred from player i to j while remaining in the strong ε -core. The associated payoff vector is a midpoint of the ε -core segment in i – j direction and is therefore a candidate that satisfies the bisection property. From these results we can determine in a sophisticated pattern-matching procedure the constraints which are needed to construct the final linear programming problem for computing at least a (pre)-kernel point of the game. From the derived final linear program large parts or the whole (pre)-kernel can be easily calculated. Finally, the program checks if the computed (pre)-kernel candidate belongs to the (pre)-kernel. In cases where the candidate does not pass the (pre)-kernel check, the function is called a further time with additional informations about the game. A further call could be necessary if the intersection set of the n 2 solution sets is empty and no correction of the final LP is applied for, in this case, for at least one distinct pair of players the largest bi-symmetrical transfer is of no importance to compute a (pre)-kernel point, that is, no candidate of the final linear problem satisfies the bisection property. This implies that at least one largest bi-symmetrical transfer δ ij ε is greater than the maximal transfer in i – j direction that is possible at a (pre)-kernel point y ⇀ while remaining in the core, that is, δ ij ε > δ ij ε ( y ⇀ ) , with y ⇀ ∈ K * ( Γ ) . Hence, if the solution intersection set is non-empty, then all payoff vectors in the intersection set possess the bisection property and are therefore (pre)-kernel elements. The (pre)-kernel of a TU-game with an empty core can be computed, for instance, by providing the epsilon value for the least-core as an additional information.

A UML profile for framework modeling

The current standard Unified Modeling Language(UML) could not model framework flexibility and extendibility adequately due to lack of appropriate constructs to distinguish framework hot spots from kernel elements. A new UML profile that may customize UML for framework modeling was presented using the extension mechanisms of UML, providing a group of UML extensions to meet the needs of framework modeling. In this profile, the extended class diagrams and sequence diagrams were defined to straightforwardly identify the hot spots and describe their instantiation restrictions. A transformation model based on design patterns was also put forward, such that the profile based framework design diagrams could be automatically mapped to the corresponding implementation diagrams. It was proved that the presented profile makes framework modeling more straightforwardly and therefore easier to understand and instantiate.

A FAST SVM TRAINING ALGORITHM

A fast support vector machine (SVM) training algorithm is proposed under SVM's decomposition framework by effectively integrating kernel caching, digest and shrinking policies and stopping conditions. Kernel caching plays a key role in reducing the number of kernel evaluations by maximal reusage of cached kernel elements. Extensive experiments have been conducted on a large handwritten digit database MNIST to show that the proposed algorithm is much faster than Keerthi et al.'s improved SMO, about nine times. Combined with principal component analysis, the total training for ten one-against-the-rest classifiers on MNIST took less than an hour. Moreover, the proposed fast algorithm speeds up SVM training without sacrificing the generalization performance. The 0.6% error rate on MNIST test set has been achieved. The promising scalability of the proposed scheme paves a new way to solve more large-scale learning problems in other domains such as data mining.

An Algebraic Multigrid Method for Linear Elasticity

We present an algebraic multigrid (AMG) method for the efficient solution of linear block-systems stemming from a discretization of a system of partial differential equations (PDEs). It generalizes the classical AMG approach for scalar problems to systems of PDEs in a natural blockwise fashion. We apply this approach to linear elasticity and show that the block interpolation, described in this paper, reproduces the rigid body modes, i.e., the kernel elements of the discrete linear elasticity operator. It is well known from geometric multigrid methods that this reproduction of the kernel elements is an essential property to obtain convergence rates which are independent of the problem size. We furthermore present results of various numerical experiments in two and three dimensions. They confirm that the method is robust with respect to variations of the Poisson ratio $\nu$. We obtain rates $\rho<0.4$ for $\nu<0.4$. These measured rates clearly show that the method provides fast convergence for a large variety of discretized elasticity problems.

The Kernel of the Adjacency Matrix of a Rectangular Mesh

Given an m × n rectangular mesh, its adjacency matrix A , having only integer entries, may be interpreted as a map between vector spaces over an arbitrary field K . We describe the kernel of A : it is a direct sum of two natural subspaces whose dimensions are equal to $\lceil c/2 \rceil$ and $\lfloor c/2 \rfloor$ , where c = gcd (m+1,n+1) - 1 . We show that there are bases to both vector spaces, with entries equal to 0,1 and -1 . When K = Z/(2), the kernel elements of these subspaces are described by rectangular tilings of a special kind. As a corollary, we count the number of tilings of a rectangle of integer sides with a specified set of tiles.

Negative order MKdV hierarchy and a new integrable Neumann-like system

The purpose of this paper is to develop the negative order MKdV hierarchy and to present a new related integrable Neumann-like Hamiltonian flow from the view point of inverse recursion operator and constraint method. The whole MKdV hierarchy both positive and negative is generated by the kernel elements of Lenard's operators pair and recursion operator. Through solving a key operator equation, the whole MKdV hierarchy is shown to have the Lax representation. In particular, some new integrable equation together with the Liouville equations, the sine-Gordon equation, and the sinh-Gordon equation are derived from the negative order MKdV hierarchy. It is very interesting that the restricted flow, corresponding to the negative order MKdV hierarchy, is just a new kind of Neumann-like system. This new Neumann-like system is obtained through restricting the MKdV spectral problem onto a symplectic submanifold and is proven to be completely integrable under the Dirac–Poisson bracket, which we define on the symplectic submanifold. Finally, with the help of the constraint between the Neumann-like system and the negative order MKdV hierarchy, all equations in the hierarchy are proven to have the parametric representations of solutions. In particular, we obtain the parametric solutions of the sine-Gordon equation and the sinh-Gordon equation.