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1
Tulkin, Tulkin, und Shokhida Nematova. „INVESTIGATION OF THE SPECTRUM OF A GENERALIZED FRIEDRICHS MODEL: NON-INTEGRAL LATTICE CASE“. Scientific Reports of Bukhara State University 3, Nr. 1 (30.01.2019): 5–11. http://dx.doi.org/10.52297/2181-1466/2019/3/1/1.
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The article investigates the essential and discrete spectrum of the self-adjoint generalized Friedrichs model. This model corresponds to a system consisting of no more than two particles on a non-integral lattice, and operates in a truncated subspace of Fock space. The number and location of eigenvalues is determined according to the "interaction parameter". Anobvious form of the eigenvectors is found
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Wang, Xinsheng, Chenxu Wang und Mingyan Yu. „The Minimum Norm Least-Squares Solution in Reduction by Krylov Subspace Methods“. Journal of Circuits, Systems and Computers 26, Nr. 01 (04.10.2016): 1750006. http://dx.doi.org/10.1142/s0218126617500062.
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In recent years, model order reduction (MOR) of interconnect system has become an important technique to reduce the computation complexity and improve the verification efficiency in the nanometer VLSI design. The Krylov subspaces techniques in existing MOR methods are efficient, and have become the methods of choice for generating small-scale macro-models of the large-scale multi-port RCL networks that arise in VLSI interconnect analysis. Although the Krylov subspace projection-based MOR methods have been widely studied over the past decade in the electrical computer-aided design community, all of them do not provide a best optimal solution in a given order. In this paper, a minimum norm least-squares solution for MOR by Krylov subspace methods is proposed. The method is based on generalized inverse (or pseudo-inverse) theory. This enables a new criterion for MOR-based Krylov subspace projection methods. Two numerical examples are used to test the PRIMA method based on the method proposed in this paper as a standard model.
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KIM, W. T., B. H. CHO und D. K. PARK. „HAMILTONIAN FORMULATION OF CHIRAL SCHWINGER MODEL IN FOUR DIMENSIONS“. Modern Physics Letters A 04, Nr. 26 (10.12.1989): 2531–37. http://dx.doi.org/10.1142/s0217732389002835.
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The four dimensional chiral Schwinger model can be quantized through the generalized point splitting method in Schrödinger representation. It satisfies the consistency and unitarity in the physical subspace.
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GANGULY, NILOY, PRADIPTA MAJI, BIPLAB K. SIKDAR und P. PAL CHAUDHURI. „GENERALIZED MULTIPLE ATTRACTOR CELLULAR AUTOMATA (GMACA) MODEL FOR ASSOCIATIVE MEMORY“. International Journal of Pattern Recognition and Artificial Intelligence 16, Nr. 07 (November 2002): 781–95. http://dx.doi.org/10.1142/s0218001402001988.
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This paper reports an efficient technique of evolving Cellular Automata (CA) as an associative memory model. The evolved CA termed as GMACA (Generalized Multiple Attractor Cellular Automata), acts as a powerful pattern recognizer. Detailed analysis of GMACA rules establishes the fact that the rule subspace of the pattern recognizing CA lies at the edge of chaos — believed to be capable of executing complex computation.
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Reynders, Edwin, und Guido De Roeck. „Subspace identification of (AR)ARMAX, Box-Jenkins, and generalized model structures“. IFAC Proceedings Volumes 42, Nr. 10 (2009): 868–73. http://dx.doi.org/10.3182/20090706-3-fr-2004.00144.
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6
Zhang, Zhiyi. „3D resistivity mapping of airborne EM data“. GEOPHYSICS 68, Nr. 6 (November 2003): 1896–905. http://dx.doi.org/10.1190/1.1635042.
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A 3D resistivity mapping technique has been developed to provide fast estimates of resistivity distributions in airborne electromagnetic surveys. This proposed 3D mapping method consists of an approximate 3D linear inverse operator and a generalized subspace solver. The 3D inverse operator can be generated using any forward approximation that is linear in resistivity. The generalized subspace method is an alternative to the conjugate gradient method, and it reduces the original large linear system of equations to a much smaller but nonlinear one that is solved iteratively. The major benefit of using generalized subspace methods is that subspace vectors can be built based upon physical principles such as skin and investigation depths. Since the 3D mapping is a linear inverse problem, no iteration, and thus no forward modeling nor sensitivity updating, is needed. The 3D resistivity‐mapping technique can be used directly to estimate 3D resistivity distribution or to provide a model update during an intermediate iteration in a nonlinear 3D inversion. Synthetic and field data examples indicate that the 3D mapping can provide quantitative information about the resistivity and spatial distributions of the 3D targets.
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Zhao, Yuhui, Jinlong Yu, Peng Shan, Ziheng Zhao, Xueying Jiang und Shuli Gao. „PLS Subspace-Based Calibration Transfer for Near-Infrared Spectroscopy Quantitative Analysis“. Molecules 24, Nr. 7 (02.04.2019): 1289. http://dx.doi.org/10.3390/molecules24071289.
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In order to enable the calibration model to be effectively transferred among multiple instruments and correct the differences between the spectra measured by different instruments, a new feature transfer model based on partial least squares regression (PLS) subspace (PLSCT) is proposed in this paper. Firstly, the PLS model of the master instrument is built, meanwhile a PLS subspace is constructed by the feature vectors. Then the master spectra and the slave spectra are projected into the PLS subspace, and the features of the spectra are also extracted at the same time. In the subspace, the pseudo predicted feature of the slave spectra is transferred by the ordinary least squares method so that it matches the predicted feature of the master spectra. Finally, a feature transfer relationship model is constructed through the feature transfer of the PLS subspace. This PLS-based subspace transfer provides an efficient method for performing calibration transfer with only a small number of standard samples. The performance of the PLSCT was compared and assessed with slope and bias correction (SBC), piecewise direct standardization (PDS), calibration transfer method based on canonical correlation analysis (CCACT), generalized least squares (GLSW), multiplicative signal correction (MSC) methods in three real datasets, statistically tested by the Wilcoxon signed rank test. The obtained experimental results indicate that PLSCT method based on the PLS subspace is more stable and can acquire more accurate prediction results.
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Mojaveri, B., A. Dehghani, M. A. Fasihi und T. Mohammadpour. „Ground state and thermal entanglement between two two-level atoms interacting with a nondegenerate parametric amplifier: Different sub-spaces“. International Journal of Modern Physics B 33, Nr. 06 (10.03.2019): 1950035. http://dx.doi.org/10.1142/s0217979219500358.
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In this paper, a Hamiltonian model that includes interaction of two coupled two-level atoms with a nondegenerate parametric amplifier in a cavity is introduced. By using the two-mode squeezing operator and under a certain condition, the introduced Hamiltonian is reduced to a generalized Jaynes–Cummings Hamiltonian. The constants of motion of system imply the existence of a decomposition of the system’s Hilbert space [Formula: see text] into a direct sum of three infinite dimensional sub-spaces, as [Formula: see text]. This decomposition enables us to study ground and thermally induced entanglement between the atoms in each of the sub-spaces as well as whole Hilbert space. The effect of atom–atom and atom–photon couplings on the degree of ground state and thermal entanglement are also investigated using the concurrence measure. It is found that in the subspaces [Formula: see text] and [Formula: see text] for all experimental values of parameters of the system, the atoms are disentangled. It is also observed that in the total space [Formula: see text] the ground state entanglement is always zero, while in the subspace [Formula: see text] it is at its maximum value. Moreover, it is found that in the subspace [Formula: see text] thermal entanglement between the atoms is robust against temperature.
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Wu, Riheng, Yangyang Dong, Zhenhai Zhang und Le Xu. „Two 2-D DOA Estimation Methods with Full and Partial Generalized Virtual Aperture Extension Technology“. International Journal of Antennas and Propagation 2019 (24.12.2019): 1–11. http://dx.doi.org/10.1155/2019/3924569.
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We address the two-dimensional direction-of-arrival (2-D DOA) estimation problem for L-shaped uniform linear array (ULA) using two kinds of approaches represented by the subspace-like method and the sparse reconstruction method. Particular interest emphasizes on exploiting the generalized conjugate symmetry property of L-shaped ULA to maximize the virtual array aperture for two kinds of approaches. The subspace-like method develops the rotational invariance property of the full virtual received data model by introducing two azimuths and two elevation selection matrices. As a consequence, the problem to estimate azimuths represented by an eigenvalue matrix can be first solved by applying the eigenvalue decomposition (EVD) to a known nonsingular matrix, and the angles pairing is automatically implemented via the associate eigenvector. For the sparse reconstruction method, first, we give a lemma to verify that the received data model is equivalent to its dictionary-based sparse representation under certain mild conditions, and the uniqueness of solutions is guaranteed by assuming azimuth and elevation indices to lie on different rows and columns of sparse signal cross-correlation matrix; we then derive two kinds of data models to reconstruct sparse 2-D DOA via M-FOCUSS with and without compressive sensing (CS) involvements; finally, the numerical simulations validate the proposed approaches outperform the existing methods at a low or moderate complexity cost.
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Liu, Xian-xia, Jiao-fen Li und Xi-Yan Hu. „Generalized inverse problems for part symmetric matrices on a subspace in structural dynamic model updating“. Mathematical and Computer Modelling 53, Nr. 1-2 (Januar 2011): 110–21. http://dx.doi.org/10.1016/j.mcm.2010.07.024.
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Smaga, Łukasz, und Hidetoshi Matsui. „A note on variable selection in functional regression via random subspace method“. Statistical Methods & Applications 27, Nr. 3 (25.01.2018): 455–77. http://dx.doi.org/10.1007/s10260-018-0421-7.
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Abstract Variable selection problem is one of the most important tasks in regression analysis, especially in a high-dimensional setting. In this paper, we study this problem in the context of scalar response functional regression model, which is a linear model with scalar response and functional regressors. The functional model can be represented by certain multiple linear regression model via basis expansions of functional variables. Based on this model and random subspace method of Mielniczuk and Teisseyre (Comput Stat Data Anal 71:725–742, 2014), two simple variable selection procedures for scalar response functional regression model are proposed. The final functional model is selected by using generalized information criteria. Monte Carlo simulation studies conducted and a real data example show very satisfactory performance of new variable selection methods under finite samples. Moreover, they suggest that considered procedures outperform solutions found in the literature in terms of correctly selected model, false discovery rate control and prediction error.
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BAUMGÄRTEL, HELLMUT. „GENERALIZED EIGENVECTORS FOR RESONANCES IN THE FRIEDRICHS MODEL AND THEIR ASSOCIATED GAMOV VECTORS“. Reviews in Mathematical Physics 18, Nr. 01 (Februar 2006): 61–78. http://dx.doi.org/10.1142/s0129055x06002589.
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A Gelfand triplet for the Hamiltonian H of the Friedrichs model on ℝ with multiplicity space [Formula: see text], [Formula: see text], is constructed such that exactly the resonances (poles of the inverse of the Livšic-matrix) are (generalized) eigenvalues of H. The corresponding eigen(anti)linear forms are calculated explicitly. Using the wave matrices for the wave (Möller) operators the corresponding eigen(anti)linear forms on the Schwartz space [Formula: see text] for the unperturbed Hamiltonian H0 are also calculated. It turns out that they are of pure Dirac type and can be characterized by their corresponding Gamov vector λ → k/(ζ0 - λ)-1, ζ0 resonance, [Formula: see text], which is uniquely determined by restriction of [Formula: see text] to [Formula: see text], where [Formula: see text] denotes the Hardy space of the upper half-plane. Simultaneously this restriction yields a truncation of the generalized evolution to the well-known decay semigroup for t ≥ 0 of the Toeplitz type on [Formula: see text]. That is: Exactly those pre-Gamov vectors λ → k/(ζ - λ)-1, ζ from the lower half-plane, [Formula: see text], have an extension to a generalized eigenvector of H if ζ is a resonance and if k is from that subspace of [Formula: see text] which is uniquely determined by its corresponding Dirac type antilinear form.
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Hernández-Cervantes, A., und R. Quezada. „Stationary states of weak coupling limit-type Markov generators and quantum transport models“. Infinite Dimensional Analysis, Quantum Probability and Related Topics 23, Nr. 01 (März 2020): 2050003. http://dx.doi.org/10.1142/s0219025720500034.
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We prove that every stationary state in the annihilator of all Kraus operators of a weak coupling limit-type Markov generator consists of two pieces, one of them supported on the interaction-free subspace and the second one on its orthogonal complement. In particular, we apply the previous result to describe in detail the structure of a slightly modified quantum transport model due to Arefeva et al. (modified AKV’s model) studied first in [J. C. García et al., Entangled and dark stationary states of excitation energy transport models in many-particles systems and photosynthesis, Infin. Dimens. Anal. Quantum Probab. Relat. Top. 21(3) (2018), Article ID: 1850018, p. 21, doi:10.1142/S0219025718500182], in terms of generalized annihilation and creation operators.
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Popov, Oleksandr, und Oleksiy Chystiakov. „On the Efficiency of Algorithms with Multi-level Parallelism“. Physico-mathematical modelling and informational technologies, Nr. 33 (05.09.2021): 133–37. http://dx.doi.org/10.15407/fmmit2021.33.133.
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The paper investigates the efficiency of algorithms for solving computational mathematics problems that use a multilevel model of parallel computing on heterogeneous computer systems. A methodology for estimating the acceleration of algorithms for computers using a multilevel model of parallel computing is proposed. As an example, the parallel algorithm of the iteration method on a subspace for solving the generalized algebraic problem of eigenvalues of symmetric positive definite matrices of sparse structure is considered. For the presented algorithms, estimates of acceleration coefficients and efficiency were obtained on computers of hybrid architecture using graphics accelerators, on multi-core computers with shared memory and multi-node computers of MIMD-architecture.
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Coyette, J. P., und K. R. Fyfe. „An Improved Formulation for Acoustic Eigenmode Extraction from Boundary Element Models“. Journal of Vibration and Acoustics 112, Nr. 3 (01.07.1990): 392–97. http://dx.doi.org/10.1115/1.2930521.
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The acoustic boundary element method has been utilized primarily as a direct response analysis technique. Recently, methodologies have been published that enable the formulation of an eigenvalue problem from a boundary element model. These techniques, however, have been very slow due to the inefficient synthesis techniques used in solving the algebraic problems. In this paper, an alternative procedure is obtained which indirectly calculates the desired acoustic variables. This technique greatly enhances the calculation speed in setting up the eigenvalue problem and in determining the field pressures. A subspace iteration technique is outlined to solve the generalized unsymmetric eigenvalue problem. Examples are presented to show the accuracy of the method.
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Kelbert, Mark, und Yurii Suhov. „A Quantum Mermin-Wagner Theorem for a Generalized Hubbard Model“. Advances in Mathematical Physics 2013 (2013): 1–20. http://dx.doi.org/10.1155/2013/637375.
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This paper is the second in a series of papers considering symmetry properties of bosonic quantum systems over 2D graphs, with continuous spins, in the spirit of the Mermin-Wagner theorem. In the model considered here the phase space of a single spin isℋ1=L2(M),whereMis ad-dimensional unit torusM=ℝd/ℤdwith a flat metric. The phase space ofkspins isℋk=L2sym(Mk), the subspace ofL2(Mk)formed by functions symmetric under the permutations of the arguments. The Fock spaceH=⊕k=0,1,…ℋkyields the phase space of a system of a varying (but finite) number of particles. We associate a spaceH≃H(i)with each vertexi∈Γof a graph(Γ,ℰ)satisfying a special bidimensionality property. (Physically, vertexirepresents a heavy “atom” or “ion” that does not move but attracts a number of “light” particles.) The kinetic energy part of the Hamiltonian includes (i)-Δ/2, the minus a half of the Laplace operator onM, responsible for the motion of a particle while “trapped” by a given atom, and (ii) an integral term describing possible “jumps” where a particle may join another atom. The potential part is an operator of multiplication by a function (the potential energy of a classical configuration) which is a sum of (a) one-body potentialsU(1)(x),x∈M, describing a field generated by a heavy atom, (b) two-body potentialsU(2)(x,y),x,y∈M, showing the interaction between pairs of particles belonging to the same atom, and (c) two-body potentialsV(x,y),x,y∈M, scaled along the graph distanced(i,j)between verticesi,j∈Γ, which gives the interaction between particles belonging to different atoms. The system under consideration can be considered as a generalized (bosonic) Hubbard model. We assume that a connected Lie groupGacts onM, represented by a Euclidean space or torus of dimensiond'≤d, preserving the metric and the volume inM. Furthermore, we suppose that the potentialsU(1),U(2), andVareG-invariant. The result of the paper is that any (appropriately defined) Gibbs states generated by the above Hamiltonian isG-invariant, provided that the thermodynamic variables (the fugacityzand the inverse temperatureβ) satisfy a certain restriction. The definition of a Gibbs state (and its analysis) is based on the Feynman-Kac representation for the density matrices.
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Liu, Chunxi, Zhikun Chen und Dongliang Peng. „Fast DOA Estimation Based on the Transform Domain Weighted Noise Subspace Fitting Algorithm for Generalized Sparse Array“. International Journal of Antennas and Propagation 2021 (23.07.2021): 1–10. http://dx.doi.org/10.1155/2021/9952575.
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Compared with uniform arrays, a generalized sparse array (GSA) can obtain larger array aperture because of its larger element spacing, which improves the accuracy of DOA estimation. At present, most DOA estimation algorithms are only suitable for the uniform arrays, while a few DOA estimate algorithms that can be applied to the GSA are unsatisfactory in terms of computational speed and accuracy. To compensate this deficiency, an improved DOA estimation algorithm which can be applied to the GSA is proposed in this paper. First, the received signal model of the GSA is established. Then, a fast DOA estimation method is derived by combining the weighted noise subspace algorithm (WNSF) with the concept of “transform domain” (TD). Theoretical analysis and simulation results show that compared with the traditional multiple signal classification (MUSIC) algorithm and the traditional WNSF algorithm, the proposed algorithm has higher accuracy and lower computational complexity.
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Pelling, Art J. R., und Ennes Sarradj. „Efficient Forced Response Computations of Acoustical Systems with a State-Space Approach“. Acoustics 3, Nr. 3 (11.08.2021): 581–94. http://dx.doi.org/10.3390/acoustics3030037.
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State-space models have been successfully employed for model order reduction and control purposes in acoustics in the past. However, due to the cubic complexity of the singular value decomposition, which makes up the core of many subspace system identification (SSID) methods, the construction of large scale state-space models from high-dimensional measurement data has been problematic in the past. Recent advances of numerical linear algebra have brought forth computationally efficient randomized rank-revealing matrix factorizations and it has been shown that these factorizations can be used to enhance SSID methods such as the Eigensystem Realization Algorithm (ERA). In this paper, we demonstrate the applicability of the so-called generalized ERA to acoustical systems and high-dimensional input data by means of an example. Furthermore, we introduce a new efficient method of forced response computation that relies on a state-space model in quasi-diagonal form. Numerical experiments reveal that our proposed method is more efficient than previous state-space methods and can even outperform frequency domain convolutions in certain scenarios.
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Barrios, José Angel, F. Sanchez, Francisco Gonzalez-Longatt und Gianfranco Claudio. „System identification applied to a single area electric power system under frequency response“. Indonesian Journal of Electrical Engineering and Computer Science 22, Nr. 3 (01.06.2021): 1236. http://dx.doi.org/10.11591/ijeecs.v22.i3.pp1236-1244.
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This research paper proposes a methodology to apply identification methods to find a simplified model of three different governors in a single area electric power system (SAEPS). A SAEPS with different governors-turbine is presented: a hydraulic turbine, a steam turbine and a steam reheat turbine. In this same investigation, an analytic reduction has been performed, a fifth order system was found analytically, thus a transfer function equivalent to the three different governor-turbine elements was obtained, this equivalent transfer function models the complete behavior of the three devices. Two systems identification (SI) algorithms have been proposed to apply them to this generic subspace state-space (N4SID) and generalized poisson moment functionals (GPMF) electrical system, these presented similar results. The results of the performance and simulation analysis exhibit that using the SI technique, fifth, fourth and third-order systems were obtained that graphically show a very small estimation error compared to the original signal, this fact could be check simulating the simplified models using the same input-output data. The results are presented in a table that shows a comparison of the model respond the fifth, fourth, third and second-order systems.
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KHRENNIKOV, A. YU, V. M. SHELKOVICH und O. G. SMOLYANOV. „LOCALLY CONVEX SPACES OF VECTOR-VALUED DISTRIBUTIONS WITH MULTIPLICATIVE STRUCTURES“. Infinite Dimensional Analysis, Quantum Probability and Related Topics 05, Nr. 04 (Dezember 2002): 483–502. http://dx.doi.org/10.1142/s0219025702001000.
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We construct an infinite-dimensional linear space [Formula: see text] of vector-valued distributions (generalized functions), or sequences, f*(x)=(fn(x)) finite from the left (i.e. fn(x)=0 for n<n0(f*)) whose components fn(x) belong to the linear span [Formula: see text] generated by the distributions δ(m-1)(x-ck), P((x-ck)-m), xm-1, where m=1, 2, …, ck ∈ ℝ, k = 1, …, s. The space of distributions [Formula: see text] can be realized as a subspace in [Formula: see text] This linear space [Formula: see text] has the structure of an associative and commutative algebra containing a unity element and free of zero divizors. The Schwartz counterexample does not hold in the algebra [Formula: see text]. Unlike the Colombeau algebra, whose elements have no explicit functional interpretation, elements of the algebra [Formula: see text] are infinite-dimensional Schwartz vector-valued distributions. This construction can be considered as a next step and a "model" on the way of constructing a nonlinear theory of distributions similar to that developed by L. Schwartz. The obtained results can be considerably generalized.
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Liang, Jun, Minzhe Li, Zhongliang Jing und Han Pan. „Multi-Target Joint Detection; Tracking and Classification Based on Marginal GLMB Filter and Belief Function Theory“. Sensors 20, Nr. 15 (29.07.2020): 4235. http://dx.doi.org/10.3390/s20154235.
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This paper proposes a new solution to multi-target joint detection, tracking and classification based on labeled random finite set (RFS) and belief function theory. A class dependent multi-model marginal generalized labeled multi-Bernoulli (MGLMB) filter is developed to analytically calculate the multi-target number, state estimates and model probabilities. In addition, a two-level classifier based on continuous transferable belief model (cTBM) is designed for target classification. To make full use of the kinematic characteristics for classification, both the dynamic modes and states are considered in the classifier, the model dependent class beliefs are computed on the continuous state feature subspace corresponding to different dynamic modes and then fused. As a result that the uncertainty about the classes is well described for decision, the classification results are more reasonable and robust. Moreover, as the estimation and classification problems are jointly solved, the tracking and classification performance are both improved. In the simulation, a scenario contains multi-target with miss detection and dense clutter is used. The performance of multi-target detection, tracking and classification is better than traditional methods based on Bayesian classifier or single model. Simulation results are illustrated to demonstrate the effectiveness and superiority of the proposed algorithm.
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Goykhman, Yuriy, und Mahta Moghaddam. „Retrieval of Parameters for Three-Layer Media with Nonsmooth Interfaces for Subsurface Remote Sensing“. International Journal of Antennas and Propagation 2012 (2012): 1–12. http://dx.doi.org/10.1155/2012/563730.
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A solution to the inverse problem for a three-layer medium with nonsmooth boundaries, representing a large class of natural subsurface structures, is developed in this paper using simulated radar data. The retrieval of the layered medium parameters is accomplished as a sequential nonlinear optimization starting from the top layer and progressively characterizing the layers below. The optimization process is achieved by an iterative technique built around the solution of the forward scattering problem. The forward scattering process is formulated by using the extended boundary condition method (EBCM) and constructing reflection and transmission matrices for each interface. These matrices are then combined into the generalized scattering matrix for the entire system, from which radar scattering coefficients are then computed. To be efficiently utilized in the inverse problem, the forward scattering model is simulated over a wide range of unknowns to obtain a complete set of subspace-based equivalent closed-form models that relate radar backscattering coefficients to the sought-for parameters including dielectric constants of each layer and separation of the layers. The inversion algorithm is implemented as a modified conjugate-gradient-based nonlinear optimization. It is shown that this technique results in accurate retrieval of surface and subsurface parameters, even in the presence of noise.
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Hu, Zixiang, Shi Zhang, Yun Zhang, Huamin Zhou und Dequn Li. „An efficient preconditioned Krylov subspace method for large-scale finite element equations with MPC using Lagrange multiplier method“. Engineering Computations 31, Nr. 7 (30.09.2014): 1169–97. http://dx.doi.org/10.1108/ec-03-2013-0077.
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Purpose – The purpose of this paper is to propose an efficient iterative method for large-scale finite element equations of bad numerical stability arising from deformation analysis with multi-point constraint using Lagrange multiplier method. Design/methodology/approach – In this paper, taking warpage analysis of polymer injection molding based on surface model as an example, the performance of several popular Krylov subspace methods, including conjugate gradient, BiCGSTAB and generalized minimal residual (GMRES), with diffident Incomplete LU (ILU)-type preconditions is investigated and compared. For controlling memory usage, GMRES(m) is also considered. And the ordering technique, commonly used in the direct method, is introduced into the presented iterative method to improve the preconditioner. Findings – It is found that the proposed preconditioned GMRES method is robust and effective for solving problems considered in this paper, and approximate minimum degree (AMD) ordering is most beneficial for the reduction of fill-ins in the ILU preconditioner and acceleration of the convergence, especially for relatively accurate ILU-type preconditioning. And because of concerns about memory usage, GMRES(m) is a good choice if necessary. Originality/value – In this paper, for overcoming difficulties of bad numerical stability resulting from Lagrange multiplier method, together with increasing scale of problems in engineering applications and limited hardware conditions of computer, a stable and efficient preconditioned iterative method is proposed for practical purpose. Before the preconditioning, AMD reordering, commonly used in the direct method, is introduced to improve the preconditioner. The numerical experiments show the good performance of the proposed iterative method for practical cases, which is implemented in in-house and commercial codes on PC.
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Bartecki, K. „PCA-based approximation of a class of distributed parameter systems: classical vs. neural network approach“. Bulletin of the Polish Academy of Sciences: Technical Sciences 60, Nr. 3 (01.12.2012): 651–60. http://dx.doi.org/10.2478/v10175-012-0077-7.
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Abstract In this article, an approximation of the spatiotemporal response of a distributed parameter system (DPS) with the use of the principal component analysis (PCA) is considered. Based on a data obtained by the numerical solution of a set of partial differential equations, a PCA-based approximation procedure is performed. It consists in the projection of the original data into the subspace spanned by the eigenvectors of the data covariance matrix, corresponding to its highest eigenvalues. The presented approach is carried out using both the classical PCA method as well as two different neural network structures: two-layer feed-forward network with supervised learning (FF-PCA) and single-layer network with unsupervised, generalized Hebbian learning rule (GHA-PCA). In each case considered, the effect of the approximation model structure represented by the number of eigenvectors (or, in the neural case, units in the network projection layer) on the mean square approximation error of the spatiotemporal response and on the data compression ratio is analysed. As shown in the paper, the best approximation quality is obtained for the classical PCA method as well as for the FF-PCA neural approach. On the other hand, an adaptive learning method for the GHA-PCA network allows to use it in e.g. an on-line identification scheme.
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Naboko, S., und I. Wood. „The Detectable Subspace for the Friedrichs Model: Applications of Toeplitz Operators and the Riesz–Nevanlinna Factorisation Theorem“. Annales Henri Poincaré 21, Nr. 10 (13.07.2020): 3141–56. http://dx.doi.org/10.1007/s00023-020-00935-z.
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Abstract We discuss how much information on a Friedrichs model operator (a finite rank perturbation of the operator of multiplication by the independent variable) can be detected from ‘measurements on the boundary’. The framework of boundary triples is used to introduce the generalised Titchmarsh–Weyl M-function and the detectable subspaces which are associated with the part of the operator which is ‘accessible from boundary measurements’. In this paper, we choose functions arising as parameters in the Friedrichs model in certain Hardy classes. This allows us to determine the detectable subspace by using the canonical Riesz–Nevanlinna factorisation of the symbol of a related Toeplitz operator.
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Oldenburg, Douglas W., und Yaoguo Li. „Inversion of induced polarization data“. GEOPHYSICS 59, Nr. 9 (September 1994): 1327–41. http://dx.doi.org/10.1190/1.1443692.
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We develop three methods to invert induced polarization (IP) data. The foundation for our algorithms is an assumption that the ultimate effect of chargeability is to alter the effective conductivity when current is applied. This assumption, which was first put forth by Siegel and has been routinely adopted in the literature, permits the IP responses to be numerically modeled by carrying out two forward modelings using a DC resistivity algorithm. The intimate connection between DC and IP data means that inversion of IP data is a two‐step process. First, the DC potentials are inverted to recover a background conductivity. The distribution of chargeability can then be found by using any one of the three following techniques: (1) linearizing the IP data equation and solving a linear inverse problem, (2) manipulating the conductivities obtained after performing two DC resistivity inversions, and (3) solving a nonlinear inverse problem. Our procedure for performing the inversion is to divide the earth into rectangular prisms and to assume that the conductivity σ and chargeability η are constant in each cell. To emulate complicated earth structure we allow many cells, usually far more than there are data. The inverse problem, which has many solutions, is then solved as a problem in optimization theory. A model objective function is designed, and a “model” (either the distribution of σ or η)is sought that minimizes the objective function subject to adequately fitting the data. Generalized subspace methodologies are used to solve both inverse problems, and positivity constraints are included. The IP inversion procedures we design are generic and can be applied to 1-D, 2-D, or 3-D earth models and with any configuration of current and potential electrodes. We illustrate our methods by inverting synthetic DC/IP data taken over a 2-D earth structure and by inverting dipole‐dipole data taken in Quebec.
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Xu, Shuo, und Xin An. „ML2S-SVM: multi-label least-squares support vector machine classifiers“. Electronic Library 37, Nr. 6 (09.12.2019): 1040–58. http://dx.doi.org/10.1108/el-09-2019-0207.
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Purpose Image classification is becoming a supporting technology in several image-processing tasks. Due to rich semantic information contained in the images, it is very popular for an image to have several labels or tags. This paper aims to develop a novel multi-label classification approach with superior performance. Design/methodology/approach Many multi-label classification problems share two main characteristics: label correlations and label imbalance. However, most of current methods are devoted to either model label relationship or to only deal with unbalanced problem with traditional single-label methods. In this paper, multi-label classification problem is regarded as an unbalanced multi-task learning problem. Multi-task least-squares support vector machine (MTLS-SVM) is generalized for this problem, renamed as multi-label LS-SVM (ML2S-SVM). Findings Experimental results on the emotions, scene, yeast and bibtex data sets indicate that the ML2S-SVM is competitive with respect to the state-of-the-art methods in terms of Hamming loss and instance-based F1 score. The values of resulting parameters largely influence the performance of ML2S-SVM, so it is necessary for users to identify proper parameters in advance. Originality/value On the basis of MTLS-SVM, a novel multi-label classification approach, ML2S-SVM, is put forward. This method can overcome the unbalanced problem but also explicitly models arbitrary order correlations among labels by allowing multiple labels to share a subspace. In addition, the multi-label classification approach has a wider range of applications. That is to say, it is not limited to the field of image classification.
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Wu, Tao, Yiwen Li, Zhenghong Deng, Bo Feng und Xinping Ma. „Parameter Estimation for Two-Dimensional Incoherently Distributed Source with Double Cross Arrays“. Sensors 20, Nr. 16 (14.08.2020): 4562. http://dx.doi.org/10.3390/s20164562.
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A direction of arrival (DOA) estimator for two-dimensional (2D) incoherently distributed (ID) sources is presented under proposed double cross arrays, satisfying both the small interval of parallel linear arrays and the aperture equalization in the elevation and azimuth dimensions. First, by virtue of a first-order Taylor expansion for array manifold vectors of parallel linear arrays, the received signal of arrays can be reconstructed by the products of generalized manifold matrices and extended signal vectors. Then, the rotating invariant relations concerning the nominal elevation and azimuth are derived. According to the rotating invariant relationships, the rotating operators are obtained through the subspace of the covariance matrix of the received vectors. Last, the angle matching approach and angular spreads are explored based on the Capon principle. The proposed method for estimating the DOA of 2D ID sources does not require a spectral search and prior knowledge of the angular power density function. The proposed DOA estimation has a significant advantage in terms of computational cost. Investigating the influence of experimental conditions and angular spreads on estimation, numerical simulations are carried out to validate the effectiveness of the proposed method. The experimental results show that the algorithm proposed in this paper has advantages in terms of estimation accuracy, with a similar number of sensors and the same experimental conditions when compared with existing methods, and that it shows a robustness in cases of model mismatch.
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Wang, Dan, Ahmed H. Tewfik, Yingchun Zhang und Yunhe Shen. „Sparse Representation of Deformable 3D Organs with Spherical Harmonics and Structured Dictionary“. International Journal of Biomedical Imaging 2011 (2011): 1–17. http://dx.doi.org/10.1155/2011/658930.
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This paper proposed a novel algorithm to sparsely represent a deformable surface (SRDS) with low dimensionality based on spherical harmonic decomposition (SHD) and orthogonal subspace pursuit (OSP). The key idea in SRDS method is to identify the subspaces from a training data set in the transformed spherical harmonic domain and then cluster each deformation into the best-fit subspace for fast and accurate representation. This algorithm is also generalized into applications of organs with both interior and exterior surfaces. To test the feasibility, we first use the computer models to demonstrate that the proposed approach matches the accuracy of complex mathematical modeling techniques and then both ex vivo and in vivo experiments are conducted using 3D magnetic resonance imaging (MRI) scans for verification in practical settings. All results demonstrated that the proposed algorithm features sparse representation of deformable surfaces with low dimensionality and high accuracy. Specifically, the precision evaluated as maximum error distance between the reconstructed surface and the MRI ground truth is better than 3 mm in real MRI experiments.
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Cheng, Lin, Fei Tong, Jie Yang und Dongjian Zheng. „Online Modal Identification of Concrete Dams Using the Subspace Tracking-Based Method“. Shock and Vibration 2019 (23.04.2019): 1–18. http://dx.doi.org/10.1155/2019/7513261.
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To investigate the time-varying dynamic characteristics of concrete dams under the excitation of large earthquakes for online structural health monitoring and damage evaluation, an online modal identification procedure based on strong-motion records is proposed. The online modal identification of concrete dams is expressed as a subspace tracking problem, and a newly developed recursive stochastic subspace identification (RSSI) method based on the generalized yet another subspace tracker (GYAST) algorithm, which exploits both the accuracy of the subspace identification and fast computational capability, is used to extract the time-varying modal parameters of concrete dams during earthquakes. With the simulated vibration response records, a numerical example is used to verify the accuracy, robustness, and efficiency of the proposed GYAST-based, time-varying modal identification method. Then, the realistic strong-motion records of the Pacoima arch dam are analysed using the proposed modal identification procedure, and the time-varying characteristics of the concrete arch dam during three different earthquakes are analysed.
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Stankovic, Bogoljub. „Solution of mathematical models by localization“. Bulletin: Classe des sciences mathematiques et natturalles 123, Nr. 27 (2002): 1–17. http://dx.doi.org/10.2298/bmat0227001s.
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A definition of the Laplace transform of elements of D'?(?) of a subspace of distributions is given which can successfully be ap?plied to solve in a prescribed domain linear equations with derivatives, par?tial derivatives fractional derivatives and convolutions, all with initial or boundary conditions, regardless of the existence of classical or generalized solutions.
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Zhang, Liang, Bingpeng Ma, Guorong Li, Qingming Huang und Qi Tian. „Generalized Semi-supervised and Structured Subspace Learning for Cross-Modal Retrieval“. IEEE Transactions on Multimedia 20, Nr. 1 (Januar 2018): 128–41. http://dx.doi.org/10.1109/tmm.2017.2723841.
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OZAWA, MASANAO. „ORTHOMODULAR-VALUED MODELS FOR QUANTUM SET THEORY“. Review of Symbolic Logic 10, Nr. 4 (05.06.2017): 782–807. http://dx.doi.org/10.1017/s1755020317000120.
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AbstractIn 1981, Takeuti introduced quantum set theory by constructing a model of set theory based on quantum logic represented by the lattice of closed linear subspaces of a Hilbert space in a manner analogous to Boolean-valued models of set theory, and showed that appropriate counterparts of the axioms of Zermelo–Fraenkel set theory with the axiom of choice (ZFC) hold in the model. In this paper, we aim at unifying Takeuti’s model with Boolean-valued models by constructing models based on general complete orthomodular lattices, and generalizing the transfer principle in Boolean-valued models, which asserts that every theorem in ZFC set theory holds in the models, to a general form holding in every orthomodular-valued model. One of the central problems in this program is the well-known arbitrariness in choosing a binary operation for implication. To clarify what properties are required to obtain the generalized transfer principle, we introduce a class of binary operations extending the implication on Boolean logic, called generalized implications, including even nonpolynomially definable operations. We study the properties of those operations in detail and show that all of them admit the generalized transfer principle. Moreover, we determine all the polynomially definable operations for which the generalized transfer principle holds. This result allows us to abandon the Sasaki arrow originally assumed for Takeuti’s model and leads to a much more flexible approach to quantum set theory.
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Kiderlen, Markus. „On projected thick sections of stationary point processes and Boolean models“. Advances in Applied Probability 28, Nr. 02 (Juni 1996): 335. http://dx.doi.org/10.1017/s0001867800048308.
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For a stationary point process X of convex particles in ℝ d the projected thick section process X(L) on a q-dimensional linear subspace L is considered. Formulae connecting geometric functionals, e.g. the quermass densities of X and X(L), are presented. They generalize the classical results of Miles (1976) and Davy (1976) which hold only in the isotropic case.
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Kiderlen, Markus. „On projected thick sections of stationary point processes and Boolean models“. Advances in Applied Probability 28, Nr. 2 (Juni 1996): 335. http://dx.doi.org/10.2307/1428046.
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For a stationary point process X of convex particles in ℝd the projected thick section process X(L) on a q-dimensional linear subspace L is considered. Formulae connecting geometric functionals, e.g. the quermass densities of X and X(L), are presented. They generalize the classical results of Miles (1976) and Davy (1976) which hold only in the isotropic case.
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Kovalenko, Andriy. „Multiscale modeling of solvation in chemical and biological nanosystems and in nanoporous materials“. Pure and Applied Chemistry 85, Nr. 1 (04.01.2013): 159–99. http://dx.doi.org/10.1351/pac-con-12-06-03.
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Statistical–mechanical, 3D-RISM-KH molecular theory of solvation (3D reference interaction site model with the Kovalenko–Hirata closure) is promising as an essential part of multiscale methodology for chemical and biomolecular nanosystems in solution. 3D-RISM-KH explains the molecular mechanisms of self-assembly and conformational stability of synthetic organic rosette nanotubes (RNTs), aggregation of prion proteins and β-sheet amyloid oligomers, protein-ligand binding, and function-related solvation properties of complexes as large as the Gloeobacter violaceus pentameric ligand-gated ion channel (GLIC) and GroEL/ES chaperone. Molecular mechanics/Poisson–Boltzmann (generalized Born) surface area [MM/PB(GB)SA] post-processing of molecular dynamics (MD) trajectories involving SA empirical nonpolar terms is replaced with MM/3D-RISM-KH statistical–mechanical evaluation of the solvation thermodynamics. 3D-RISM-KH has been coupled with multiple time-step (MTS) MD of the solute biomolecule driven by effective solvation forces, which are obtained analytically by converging the 3D-RISM-KH integral equations at outer time-steps and are calculated in between by using solvation force coordinate extrapolation (SFCE) in the subspace of previous solutions to 3D-RISM-KH. The procedure is stabilized by the optimized isokinetic Nosé–Hoover (OIN) chain thermostatting, which enables gigantic outer time-steps up to picoseconds to accurately calculate equilibrium properties. The multiscale OIN/SFCE/3D-RISM-KH algorithm is implemented in the Amber package and illustrated on a fully flexible model of alanine dipeptide in aqueous solution, exhibiting the computational rate of solvent sampling 20 times faster than standard MD with explicit solvent. Further substantial acceleration can be achieved with 3D-RISM-KH efficiently sampling essential events with rare statistics such as exchange and localization of solvent, ions, and ligands at binding sites and pockets of the biomolecule. 3D-RISM-KH was coupled with ab initio complete active space self-consistent field (CASSCF) and orbital-free embedding (OFE) Kohn–Sham (KS) density functional theory (DFT) quantum chemistry methods in an SCF description of electronic structure, optimized geometry, and chemical reactions in solution. The (OFE)KS-DFT/3D-RISM-KH multi-scale method is implemented in the Amsterdam Density Functional (ADF) package and extensively validated against experiment for solvation thermochemistry, photochemistry, conformational equilibria, and activation barriers of various nanosystems in solvents and ionic liquids (ILs). Finally, the replica RISM-KH-VM molecular theory for the solvation structure, thermodynamics, and electrochemistry of electrolyte solutions sorbed in nanoporous materials reveals the molecular mechanisms of sorption and supercapacitance in nanoporous carbon electrodes, which is drastically different from a planar electrical double layer.
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Mutny, Mojmir, Johannes Kirschner und Andreas Krause. „Experimental Design for Optimization of Orthogonal Projection Pursuit Models“. Proceedings of the AAAI Conference on Artificial Intelligence 34, Nr. 06 (03.04.2020): 10235–42. http://dx.doi.org/10.1609/aaai.v34i06.6585.
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Bayesian optimization and kernelized bandit algorithms are widely used techniques for sequential black box function optimization with applications in parameter tuning, control, robotics among many others. To be effective in high dimensional settings, previous approaches make additional assumptions, for example on low-dimensional subspaces or an additive structure. In this work, we go beyond the additivity assumption and use an orthogonal projection pursuit regression model, which strictly generalizes additive models. We present a two-stage algorithm motivated by experimental design to first decorrelate the additive components. Subsequently, the bandit optimization benefits from the statistically efficient additive model. Our method provably decorrelates the fully additive model and achieves optimal sublinear simple regret in terms of the number of function evaluations. To prove the rotation recovery, we derive novel concentration inequalities for linear regression on subspaces. In addition, we specifically address the issue of acquisition function optimization and present two domain dependent efficient algorithms. We validate the algorithm numerically on synthetic as well as real-world optimization problems.
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Kangal, Fatih, und Emre Mengi. „Nonsmooth algorithms for minimizing the largest eigenvalue with applications to inner numerical radius“. IMA Journal of Numerical Analysis 40, Nr. 4 (13.11.2019): 2342–76. http://dx.doi.org/10.1093/imanum/drz041.
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Abstract Nonsmoothness at optimal points is a common phenomenon in many eigenvalue optimization problems. We consider two recent algorithms to minimize the largest eigenvalue of a Hermitian matrix dependent on one parameter, both proven to be globally convergent unaffected by nonsmoothness. One of these algorithms models the eigenvalue function with a piece-wise quadratic function and is effective in dealing with nonconvex problems. The other algorithm projects the Hermitian matrix into subspaces formed of eigenvectors and is effective in dealing with large-scale problems. We generalize the latter slightly to cope with nonsmoothness. For both algorithms we analyze the rate of convergence in the nonsmooth setting, when the largest eigenvalue is multiple at the minimizer and zero is strictly in the interior of the generalized Clarke derivative, and prove that both algorithms converge rapidly. The algorithms are applied to, and the deduced results are illustrated on the computation of the inner numerical radius, the modulus of the point on the boundary of the field of values closest to the origin, which carries significance for instance for the numerical solution of a symmetric definite generalized eigenvalue problem and the iterative solution of a saddle point linear system.
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Vazifedan, Mehdi, und Qiji Jim Zhu. „No-Arbitrage Principle in Conic Finance“. Risks 8, Nr. 2 (19.06.2020): 66. http://dx.doi.org/10.3390/risks8020066.
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In a one price economy, the Fundamental Theorem of Asset Pricing (FTAP) establishes that no-arbitrage is equivalent to the existence of an equivalent martingale measure. Such an equivalent measure can be derived as the normal unit vector of the hyperplane that separates the attainable gain subspace and the convex cone representing arbitrage opportunities. However, in two-price financial models (where there is a bid–ask price spread), the set of attainable gains is not a subspace anymore. We use convex optimization, and the conic property of this region to characterize the “no-arbitrage” principle in financial models with the bid–ask price spread present. This characterization will lead us to the generation of a set of price factor random variables. Under such a set, we can find the lower and upper bounds (supper-hedging and sub-hedging bounds) for the price of any future cash flow. We will show that for any given cash flow, for which the price is outside the above range, we can build a trading strategy that provides one with an arbitrage opportunity. We will generalize this structure to any two-price finite-period financial model.
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ARAI, ASAO. „GENERALIZED WEAK WEYL RELATION AND DECAY OF QUANTUM DYNAMICS“. Reviews in Mathematical Physics 17, Nr. 09 (Oktober 2005): 1071–109. http://dx.doi.org/10.1142/s0129055x05002479.
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Let H be a self-adjoint operator on a Hilbert space [Formula: see text], T be a symmetric operator on [Formula: see text] and K(t)(t ∈ ℝ) be a bounded self-adjoint operator on [Formula: see text]. We say that (T, H, K) obeys the generalized weak Weyl relation (GWWR) if e-itHD(T) ⊂ D(T) for all t ∈ ℝ and Te-itHψ = e-itH(T+K(t))ψ, ∀ψ ∈ D(T) (D(T) denotes the domain of T). In the context of quantum mechanics where H is the Hamiltonian of a quantum system, we call T a generalized time operator of H. We first investigate, in an abstract framework, mathematical structures and properties of triples (T, H, K) obeying the GWWR. These include the absolute continuity of the spectrum of H restricted to a closed subspace of [Formula: see text], an uncertainty relation between H and T (a "time-energy uncertainty relation"), the decay property of transition probabilities |〈ψ,e-itHϕ〉|2 as |t| → ∞ for all vectors ψ and ϕ in a subspace of [Formula: see text], where 〈·,·〉 denotes the inner product of [Formula: see text]. We describe methods to construct various examples of triples (T, H, K) obeying the GWWR. In particular, we show that there exist generalized time operators of second quantization operators on Fock spaces (full Fock spaces, boson Fock spaces and fermion Fock spaces) which may have applications to quantum field models with interactions.
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Moroz, Alexander. „Generalized Rabi models: Diagonalization in the spin subspace and differential operators of Dunkl type“. EPL (Europhysics Letters) 113, Nr. 5 (01.03.2016): 50004. http://dx.doi.org/10.1209/0295-5075/113/50004.
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Gou, Xu, Wei Lu, Yi Wang, Binyu Yan und Mulin Xin. „Fisher-discriminative regularized latent sparse transfer model“. International Journal of Wavelets, Multiresolution and Information Processing 17, Nr. 03 (Mai 2019): 1950011. http://dx.doi.org/10.1142/s0219691319500115.
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Top performing algorithms are trained on massive amounts of labeled data. Alternatively, domain adaptation (DA) provides an attractive way to address the few labeled tasks when the labeled data from a different but related domain are available. Motivated by Fisher criterion, we present the novel discriminative regularization term on the latent subspace which incorporates the latent sparse domain transfer (LSDT) model in a unified framework. The key underlying idea is to make samples from one class closer and farther away from different class samples. However, it is nontrivial to design the efficient optimization algorithm. Instead, we construct a convex surrogate relaxation optimization constraint to ease this issue by alternating direction method of multipliers (ADMM) algorithm. Subsequently, we generalize our model in the reproduced kernel Hilbert space (RKHS) for tracking the nonlinear domain shift. Empirical studies demonstrate the performance improvement on the benchmark vision dataset Caltech-4DA.
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Zehn, M. W. „A Combination of Modal Synthesis and Subspace Iteration for an Efficient Algorithm for Modal Analysis within a FE-Code“. Shock and Vibration 10, Nr. 1 (2003): 27–35. http://dx.doi.org/10.1155/2003/147898.
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Various well-known modal synthesis methods exist in the literature, which are all based upon certain assumptions for the relation of generalised modal co-ordinates with internal modal co-ordinates. If employed in a dynamical FE substructure/superelement technique the generalised modal co-ordinates are represented by the master degrees of freedom (DOF) of the master nodes of the substructure. To conduct FE modal analysis the modal synthesis method can be integrated to reduce the number of necessary master nodes or to ease the process of defining additional master points within the structure. The paper presents such a combined method, which can be integrated very efficiently and seamless into a special subspace eigenvalue problem solver with no need to alter the FE system matrices within the FE code. Accordingly, the merits of using the new algorithm are the easy implementation into a FE code, the less effort to carry out modal synthesis, and the versatility in dealing with superelements. The paper presents examples to illustrate the proper work of the algorithm proposed.
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A.V., Chistyakov. „On improving the efficiency of mathematical modeling of the problem of stability of construction“. Artificial Intelligence 25, Nr. 3 (10.10.2020): 27–36. http://dx.doi.org/10.15407/jai2020.03.027.
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Algorithmic software for mathematical modeling of structural stability is considered, which is reduced to solving a partial generalized eigenvalues problem of sparse matrices, with automatic parallelization of calculations on modern parallel computers with graphics processors. Peculiarities of realization of parallel algorithms for different structures of sparse matrices are presented. The times of solving the problem of stability of composite materialsusing a three-dimensional model of "finite size fibers" on computers of different architectures are given. In mathematical modeling of physical and technical processes in many cases there is a need to solve problems of algebraic problem of eigenvalues (APVZ) with sparse matrices of large volumes. In particular, such problems arise in the analysis of the strength of structures in civil and industrial construction, aircraft construction, electric welding, etc. The solving to these problems is to determine the eigenvalues and eigenvectors of sparse matrices of different structure. The efficiency of solving these problems largely depends on the effectiveness of mathematical modeling of the problem as a whole. Continuous growth of task parameters, calculation of more complete models of objects and processes on computers require an increase in computer productivity. High-performance computing requirements are far ahead of traditional parallel computing, even with multicore processors. High-performance computing requirements are far ahead of traditional parallel computing, even with multicore processors. Today, this problem is solved by using powerful supercomputers of hybrid architecture, such as computers with multicore processors (CPUs) and graphics processors (GPUs), which combine MIMD and SIMD architectures. But the potential of high-performance computers can be used to the fullest only with algorithmic software that takes into account both the properties of the task and the features of the hybrid architecture. Complicating the architecture of modern high-performance supercomputers of hybrid architecture, which are actively used for mathematical modeling (increasing the number of computer processors and cores, different types of computer memory, different programming technologies, etc.) means a significant complication of efficient use of these resources in creating parallel algorithms and programs. here are problems with the creation of algorithmic software with automatic execution of stages of work, which are associated with the efficient use of computing resources, ways to store and process sparse matrices, analysis of the reliability of computer results. This makes it possible to significantly increase the efficiency of mathematical modeling of practical problems on modern high-performance computers, as well as free users from the problems of parallelization of complex problems. he developed algorithmic software automatically implements all stages of parallel computing and processing of sparse matrices on a hybrid computer. It was used at the Institute of Mechanics named after S.P. Tymoshenko NAS of Ukraine in modeling the strength problems of composite material. A significant improvement in the time characteristics of mathematical modeling was obtained. Problems of mathematical modeling of the properties of composite materials has an important role in designing the processes of deformation and destruction of products in various subject areas. Algorithmic software for mathematical modeling of structural stability is considered, which is reduced to solving a partial generalized problem of eigen values of sparse matrices of different structure of large orders, with automatic parallelization of calculations on modern parallel computers with graphics processors. The main methodological principles and features of implementation of parallel algorithms for different structures of sparse matrices are presented, which ensure effective implementation of multilevel parallelism of a hybrid system and reduce data exchange time during the computational process. As an example of these approaches, a hybrid algorithm of the iteration method in subspace for tape and block-diagonal matrices with a frame for computers of hybrid architecture is given. Peculiarities of data decomposition for matrices of profile structure at realization of parallel algorithms are considered. The proposed approach provides automatic determination of the required topology of the hybrid computer and the optimal amount of resources for the organization of an efficient computational process. The results of testing the developed algorithmic software for problems from the collection of the University of Florida, as well as the times of solving the problem of stability of composite materials using a three-dimensional model of "finite size fibers" on computers of different architectures. The results show a significant improvement in the time characteristics of solving problems.
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Sithole, G. „INDOOR SPACE ROUTING GRAPHS: VISIBILITY, ENCODING, ENCRYPTION AND ATTENUATION“. ISPRS - International Archives of the Photogrammetry, Remote Sensing and Spatial Information Sciences XLII-4 (19.09.2018): 579–85. http://dx.doi.org/10.5194/isprs-archives-xlii-4-579-2018.
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<p><strong>Abstract.</strong> The conventional approach to path planning for indoor navigation is to infer routes from a subdivided floor map of the indoor space. The floor map describes the spatial geometry of the space. Contained in this floor map are logical units called subspaces. For the purpose of path planning the possible routes between the subspaces have to be modelled. Typical these models employing a graph structures, or skeletons, in which the interconnected subspaces (e.g., rooms, corridors, etc.) are represented as linked nodes, i.e. a graph.</p><p>This paper presents a novel method for creating generalised graphs of indoor spaces that doesn’t require the subdivision of indoor space. The method creates the generalised graph by gradually simplifying/in-setting the floor map until a graph is obtained, a process described here as chained deflation. The resulting generalised graph allows for more flexible and natural paths to be determined within the indoor environment. Importantly the method allows the indoor space to be encoded and encrypted and supplied to users in a way that emulates the use of physical keys in the real world. Another important novelty of the method is that the space described by the graph is adaptable. The space described by the graph can be deflated or inflated according to the needs of the path planning. Finally, the proposed method can be readily generalised to the third dimension.</p><p>The concept and logic of the method are explained. A full implementation of the method will be discussed in a future paper.</p>
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Yi, Xiaoyuan, Ruoyu Li, Cheng Yang, Wenhao Li und Maosong Sun. „MixPoet: Diverse Poetry Generation via Learning Controllable Mixed Latent Space“. Proceedings of the AAAI Conference on Artificial Intelligence 34, Nr. 05 (03.04.2020): 9450–57. http://dx.doi.org/10.1609/aaai.v34i05.6488.
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As an essential step towards computer creativity, automatic poetry generation has gained increasing attention these years. Though recent neural models make prominent progress in some criteria of poetry quality, generated poems still suffer from the problem of poor diversity. Related literature researches show that different factors, such as life experience, historical background, etc., would influence composition styles of poets, which considerably contributes to the high diversity of human-authored poetry. Inspired by this, we propose MixPoet, a novel model that absorbs multiple factors to create various styles and promote diversity. Based on a semi-supervised variational autoencoder, our model disentangles the latent space into some subspaces, with each conditioned on one influence factor by adversarial training. In this way, the model learns a controllable latent variable to capture and mix generalized factor-related properties. Different factor mixtures lead to diverse styles and hence further differentiate generated poems from each other. Experiment results on Chinese poetry demonstrate that MixPoet improves both diversity and quality against three state-of-the-art models.
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Morinelli, Vincenzo, und Karl-Hermann Neeb. „Covariant Homogeneous Nets of Standard Subspaces“. Communications in Mathematical Physics 386, Nr. 1 (30.03.2021): 305–58. http://dx.doi.org/10.1007/s00220-021-04046-6.
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AbstractRindler wedges are fundamental localization regions in AQFT. They are determined by the one-parameter group of boost symmetries fixing the wedge. The algebraic canonical construction of the free field provided by Brunetti–Guido–Longo (BGL) arises from the wedge-boost identification, the BW property and the PCT Theorem. In this paper we generalize this picture in the following way. Firstly, given a $$\mathbb Z_2$$ Z 2 -graded Lie group we define a (twisted-)local poset of abstract wedge regions. We classify (semisimple) Lie algebras supporting abstract wedges and study special wedge configurations. This allows us to exhibit an analog of the Haag–Kastler one-particle net axioms for such general Lie groups without referring to any specific spacetime. This set of axioms supports a first quantization net obtained by generalizing the BGL construction. The construction is possible for a large family of Lie groups and provides several new models. We further comment on orthogonal wedges and extension of symmetries.
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Kribs, D. W., R. Laflamme, D. Poulin und M. Lesosky. „Operator quantum error correction“. Quantum Information and Computation 6, Nr. 4&5 (Juli 2006): 382–99. http://dx.doi.org/10.26421/qic6.4-5-6.
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This paper is an expanded and more detailed version of the work \cite{KLP04} in which the Operator Quantum Error Correction formalism was introduced. This is a new scheme for the error correction of quantum operations that incorporates the known techniques --- i.e. the standard error correction model, the method of decoherence-free subspaces, and the noiseless subsystem method --- as special cases, and relies on a generalized mathematical framework for noiseless subsystems that applies to arbitrary quantum operations. We also discuss a number of examples and introduce the notion of "unitarily noiseless subsystems''.
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Zhao, Baigan, Yingping Huang, Hongjian Wei und Xing Hu. „Ego-Motion Estimation Using Recurrent Convolutional Neural Networks through Optical Flow Learning“. Electronics 10, Nr. 3 (20.01.2021): 222. http://dx.doi.org/10.3390/electronics10030222.
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Visual odometry (VO) refers to incremental estimation of the motion state of an agent (e.g., vehicle and robot) by using image information, and is a key component of modern localization and navigation systems. Addressing the monocular VO problem, this paper presents a novel end-to-end network for estimation of camera ego-motion. The network learns the latent subspace of optical flow (OF) and models sequential dynamics so that the motion estimation is constrained by the relations between sequential images. We compute the OF field of consecutive images and extract the latent OF representation in a self-encoding manner. A Recurrent Neural Network is then followed to examine the OF changes, i.e., to conduct sequential learning. The extracted sequential OF subspace is used to compute the regression of the 6-dimensional pose vector. We derive three models with different network structures and different training schemes: LS-CNN-VO, LS-AE-VO, and LS-RCNN-VO. Particularly, we separately train the encoder in an unsupervised manner. By this means, we avoid non-convergence during the training of the whole network and allow more generalized and effective feature representation. Substantial experiments have been conducted on KITTI and Malaga datasets, and the results demonstrate that our LS-RCNN-VO outperforms the existing learning-based VO approaches.
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Muminov, Zahriddin, Fudziah Ismail, Zainidin Eshkuvatov und Jamshid Rasulov. „On the Discrete Spectrum of a Model Operator in Fermionic Fock Space“. Abstract and Applied Analysis 2013 (2013): 1–12. http://dx.doi.org/10.1155/2013/875194.
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We consider a model operatorHassociated with a system describing three particles in interaction, without conservation of the number of particles. The operatorHacts in the direct sum of zero-, one-, and two-particle subspaces of thefermionic Fock space ℱa(L2(𝕋3))overL2(𝕋3). We admit a general form for the "kinetic" part of the HamiltonianH, which contains a parameterγto distinguish the two identical particles from the third one. (i) We find a critical valueγ*for the parameterγthat allows or forbids the Efimov effect (infinite number of bound states if the associated generalized Friedrichs model has a threshold resonance) and we prove that only forγ<γ*the Efimov effect is absent, while this effect exists for anyγ>γ*. (ii) In the caseγ>γ*, we also establish the following asymptotics for the numberN(z)of eigenvalues ofHbelowz<Emin=infσessH:limz→EminNz/logEmin-z=𝒰0γ 𝒰0γ>0, for allγ>γ*.