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PaSTiLa: Scalable Parallel Algorithm for Unsupervised Labeling of Long Time Series PaSTiLa:用于长时间序列无监督标记的可扩展并行算法
IF 0.7 Q2 MATHEMATICS Pub Date : 2024-07-19 DOI: 10.1134/s1995080224600766
M. L. Zymbler, A. I. Goglachev

Abstract

Summarization aims at discovering a small set of typical subsequences (patterns) in the given long time series that represent the whole series. Further, one can implement unsupervised labeling of the given time series by assigning each subsequence a tag that corresponds to its most similar pattern. In the previous research, we developed the PSF (Parallel Snippet-Finder) algorithm for the time series summarization on GPU, where a snippet is the given-length subsequence, which is similar to many other subsequences w.r.t. the bespoke distance measure MPdist. However, PSF is limited by the demand that the snippet length be predefined by a domain expert. In this article, we introduce the novel parallel algorithm PaSTiLa (Parallel Snippet-based Time series Labeling) that discovers snippets and produces the labeling of the given time series on an HPC cluster with GPU nodes. As opposed to its predecessor, PaSTiLa employs the automatic selection of the snippet length from the specified range through our proposed heuristic criterion. In the experiments on labeling quality over time series from the TSSB (Time Series Segmentation Benchmark) dataset, PaSTiLa outperforms state-of-the-art segmentation-based competitors in average (textrm{F}_{1}) score. In the case of long-length time series (typically more than 8–10 K points), PaSTiLa outruns the rivals. Finally, over the million-length time series, our algorithm demonstrates a close-to-linear speedup.

摘要 总结的目的是在给定的长时间序列中发现一小部分代表整个序列的典型子序列(模式)。此外,通过为每个子序列分配与其最相似模式相对应的标签,还可以对给定的时间序列进行无监督标记。在之前的研究中,我们为 GPU 上的时间序列汇总开发了 PSF(Parallel Snippet-Finder,并行片段查找)算法,其中片段是给定长度的子序列,在定制距离度量 MPdist 的作用下,它与许多其他子序列相似。然而,PSF 受限于片段长度必须由领域专家预先定义的要求。在本文中,我们将介绍一种新颖的并行算法 PaSTiLa(基于片段的并行时间序列标注),该算法能在带有 GPU 节点的高性能计算集群上发现片段并生成给定时间序列的标注。与前者相比,PaSTiLa 通过我们提出的启发式标准,从指定范围内自动选择片段长度。在对来自TSSB(时间序列分割基准)数据集的时间序列进行标注质量实验时,PaSTiLa的平均(textrm{F}_{1})得分优于基于分割技术的一流竞争对手。在长度较长的时间序列(通常超过 8-10 K 点)中,PaSTiLa 的表现超过了竞争对手。最后,在百万长度的时间序列中,我们的算法表现出了接近线性的提速。
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引用次数: 0
Statistical Modeling of the Cobb–Douglas Production Function: A Multiple Linear Regression Approach in Presence of Stable Distribution Noise 柯布-道格拉斯生产函数的统计建模:存在稳定分布噪声时的多元线性回归方法
IF 0.7 Q2 MATHEMATICS Pub Date : 2024-07-19 DOI: 10.1134/s1995080224600572
B. D. Coulibaly, G. Chaibi, M. El Khomssi

Abstract

In this work, we delved into advanced modeling of economic relationships using the Cobb–Douglas production function as a theoretical foundation. Our primary goal was to develop an innovative multiple linear regression model by introducing innovations based on the (alpha)-stable distribution. By adapting the traditional multiple linear regression model, our approach incorporates the (alpha)-stable distribution to better represent the complexity of relationships between economic variables. This modification enables a better fit for asymmetric distributions and scenarios where data exhibit heavy tails. To assess the performance of our model, we applied it to real financial data. This practical step allowed us to evaluate the effectiveness and predictive capability of our approach in a real-world context, thus offering fresh perspectives for financial data analysis.

摘要 在这项工作中,我们以柯布-道格拉斯生产函数为理论基础,深入研究了经济关系的高级建模。我们的主要目标是通过引入基于 (α)-stable 分布的创新,建立一个创新的多元线性回归模型。通过调整传统的多元线性回归模型,我们的方法纳入了(α)-稳定分布,以更好地表示经济变量之间的复杂关系。这种修改能更好地拟合非对称分布和数据显示重尾的情况。为了评估模型的性能,我们将其应用于真实的金融数据。这一实际步骤使我们能够评估我们的方法在现实世界中的有效性和预测能力,从而为金融数据分析提供新的视角。
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引用次数: 0
Mixed Problem for an Impulsive Parabolic Integro-Differential Equation with Involution and Nonlinear Conditions 带卷积和非线性条件的脉冲抛物整微分方程的混合问题
IF 0.7 Q2 MATHEMATICS Pub Date : 2024-07-19 DOI: 10.1134/s199508022460078x
A. N. Abdullozhonova, T. K. Yuldashev, A. K. Fayziyev

Abstract

In this paper, we consider an impulsive homogeneous parabolictype partial integro-differential equation with degenerate kerneland involution. With respect to spatial variable (x) is usedDirichlet boundary value conditions and spectral problem isstudied. The Fourier method of separation of variables is applied.The countable system of nonlinear functional equations is obtainedwith respect to the Fourier coefficients of unknown function.Theorem on a unique solvability of countable system of functionalequations is proved. The method of successive approximations isused in combination with the method of contraction mapping. Theunique solution of the impulsive mixed problem is obtained in theform of Fourier series. Absolutely and uniformly convergence ofFourier series is proved.

摘要 本文考虑了一个具有退化 kerneland 内卷的脉冲同调抛物型偏积分微分方程。关于空间变量 (x) 使用了 Dirichlet 边界值条件,并研究了谱问题。应用傅里叶变量分离法,得到了关于未知函数傅里叶系数的可数非线性函数方程组,证明了可数函数方程组唯一可解性定理。结合使用了连续逼近法和收缩映射法。以傅里叶级数形式得到了脉冲混合问题的唯一解。证明了傅里叶级数的绝对均匀收敛性。
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引用次数: 0
Some Aspects of Remote State Restoring in State Transfer Governed by XXZ-Hamiltonian 由 XXZ-Hamiltonian 控制的状态转移中远程状态恢复的几个方面
IF 0.7 Q2 MATHEMATICS Pub Date : 2024-07-19 DOI: 10.1134/s1995080224600596
G. A. Bochkin, S. I. Doronin, E. B. Fel’dman, E. I. Kuznetsova, I. D. Lazarev, A. N. Pechen, A. I. Zenchuk

Abstract

We consider the remote state restoring and perfect transfer of the zero-order coherence matrix (PTZ) in a spin system governed by the XXZ-Hamiltonian conserving the excitation number. The restoring tool is represented by several nonzero Larmor frequencies in the Hamiltonian. To simplify the analysis we use two approximating models including either step-wise or pulse-type time-dependence of the Larmor frequencies. Restoring in spin chains with up to 20 nodes is studied. Studying PTZ, we consider the zigzag and rectangular configurations and optimize the transfer of the 0-order coherence matrix using geometrical parameters of the communication line as well as the special unitary transformation of the extended receiver. Overall observation is that XXZ-chains require longer time for state transfer than XX-chains, which is confirmed by the analytical study of the evolution under the nearest-neighbor approximation. We demonstrate the exponential increase of the state-transfer time with the spin chain length.

摘要 我们考虑了一个自旋系统中零阶相干矩阵(PTZ)的远程状态恢复和完美转移问题,该自旋系统受守恒激励数的 XXZ-哈密顿支配。恢复工具由哈密顿中的几个非零拉莫尔频率表示。为了简化分析,我们使用了两种近似模型,包括拉莫尔频率的阶跃型或脉冲型时间依赖性。我们研究了多达 20 个节点的自旋链中的恢复。在研究 PTZ 时,我们考虑了之字形和矩形配置,并利用通信线路的几何参数以及扩展接收器的特殊单元变换优化了 0 阶相干矩阵的传输。总体观察结果表明,XXZ 链比 XX 链需要更长的状态转移时间,这一点在最近邻近似下的演化分析研究中得到了证实。我们证明了状态转移时间随自旋链长度呈指数增长。
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引用次数: 0
On the Non-local Problem for a Boussinesq Type Equations 关于布森斯克方程的非局部问题
IF 0.7 Q2 MATHEMATICS Pub Date : 2024-07-19 DOI: 10.1134/s1995080224600808
Kh. T. Dekhkonov, Yu. E. Fayziev, R. R. Ashurov

Abstract

The problem of finding a solution, satisfying the non-local condition (u(xi_{0})=alpha u(+0)+varphi) in time for the Boussinesq type equation of the form (u_{tt}+Au_{tt}+Au=f) is studied in the article. Here (alpha) and (xi_{0}), (xi_{0}in(0,T],) are the given numbers, (A:Hrightarrow H) is the self-adjoint, unbounded, positive operator defined in the Hilbert separable space (H). By using the Fourier method, it was shown that the solution to the problem exists and is unique. The effect of parameter (alpha) on the existence and uniqueness of the solution is studied in the article. The inverse problem of determining the right-hand side of the equation is also considered.

Abstract The problem of finding a solution, satisfying the non-local condition (u(xi_{0})=alpha u(+0)+varphi) in time for the Boussinesq type equation of the form (u_{tt}+Au_{tt}+Au=f) is studied in the article.这里(alpha)和(xi_{0}), (xi_{0}in(0,T],)是给定的数,(A:Hrightarrow H) 是定义在希尔伯特可分离空间 (H)中的自交、无界、正算子。通过使用傅立叶方法,证明了问题的解是存在的,并且是唯一的。文章研究了参数 (α)对解的存在性和唯一性的影响。还考虑了确定方程右边的逆问题。
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引用次数: 0
A 2D Convolution Kernel Determination Problem for the Time-Fractional Diffusion Equation 时间-分数扩散方程的二维卷积核确定问题
IF 0.7 Q2 MATHEMATICS Pub Date : 2024-07-19 DOI: 10.1134/s1995080224600857
D. K. Durdiev, M. Akylbayev, Zh. Maxumova, A. Iskakova

Abstract

In this article, two dimensional inverse problem of determining convolution kernel in the fractional diffusion equation with the time-fractional Caputo derivative is studied. To represent the solution of the direct problem, the fundamental solution of the time-fractional diffusion equation with Riemann–Liouville derivative is constructed. Using the formulas of asymptotic expansions for the fundamental solution and its derivatives, an estimate for the solution of the direct problem is obtained in terms of the norm of the unknown kernel function, which was used for studying the inverse problem. The inverse problem is reduced to the equivalent integral equation of the Volterra type. The local existence and global uniqueness results are proven by the aid of fixed point argument in suitable functional classes. Also the stability estimate is obtained.

摘要 本文研究了具有时间分数卡普托导数的分数扩散方程中确定卷积核的二维反问题。为了表示直接问题的解,构建了具有黎曼-刘维尔导数的时间分数扩散方程的基本解。利用基本解及其导数的渐近展开公式,可以根据未知核函数的规范得到直接问题解的估计值,该估计值用于研究逆问题。逆问题被简化为 Volterra 类型的等价积分方程。借助适当函数类的定点论证,证明了局部存在性和全局唯一性结果。同时还获得了稳定性估计。
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引用次数: 0
D-Stability, Strong D-Stability and $$mu$$ -Values D 级稳定性、强 D 级稳定性和 $$mu$ - 值
IF 0.7 Q2 MATHEMATICS Pub Date : 2024-07-19 DOI: 10.1134/s1995080224600754
Mutti-Ur Rehman, Tulkin H. Rasulov, Fouzia Amir

Abstract

In this article, we present some connections between the notation of D-stability, Strong D-stability, and structured singular values known as (mu)-values for square matrices.

摘要 在本文中,我们介绍了 D-稳定性、强 D-稳定性和结构奇异值之间的一些联系,这些奇异值被称为方阵的 (mu)-值。
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引用次数: 0
Asymptotics of the Solution of the Cauchy Problem with an Unstable Spectrum and Prolonging Loss of Stability 具有不稳定频谱和长期失稳的考奇问题解的渐近性
IF 0.7 Q2 MATHEMATICS Pub Date : 2024-07-19 DOI: 10.1134/s1995080224600845
D. A. Tursunov, A. S. Sadieva, K. G. Kozhobekov, E. A. Tursunov

Abstract

The article is devoted to construct a complete asymptotic expansion of the solution to the Cauchy problem for a linear analytical system of singularly perturbed ordinary differential equations of the first order. The peculiarities of the Cauchy problem are that a small parameter is present in front of the derivative, and the stability conditions are violated in the region under consideration. By modifying the method of boundary functions, a formal asymptotic expansion of the solution to the Cauchy problem is constructed. The remainder term of the expansion is estimated by the idea of L.S. Pontryagin entering the complex plane.

摘要 本文致力于构建一阶奇异扰动常微分方程线性解析系统的 Cauchy 问题解的完整渐近展开。Cauchy 问题的特殊性在于导数前存在一个小参数,并且在所考虑的区域内违反了稳定性条件。通过修改边界函数方法,构建了 Cauchy 问题解的形式渐近展开。根据 L.S. Pontryagin 进入复平面的思想,对扩展的余项进行了估计。
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引用次数: 0
Derivation of a Controllability Criteria for a Linear Singularly Perturbed Discrete System with Small Step 小步长线性奇异扰动离散系统可控性标准的推导
IF 0.7 Q2 MATHEMATICS Pub Date : 2024-07-19 DOI: 10.1134/s1995080224600547
B. Y. Ashirbaev, T. K. Yuldashev

Abstract

The article is devoted to study of controllability properties of a linear singularly perturbed discrete system with a small step. It is used the Gram operator, which transforms an infinite-dimensional space into a finite-dimensional one, and based on the separation of state variables of a linear discrete singularly perturbed system with a small step. The controllability criteria for this discrete system is derived.

摘要 本文致力于研究具有小步长的线性奇异扰动离散系统的可控性。文章使用了将无穷维空间转换为有限维空间的格拉姆算子,并基于具有小步长的线性离散奇异扰动系统的状态变量分离。得出了该离散系统的可控性标准。
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引用次数: 0
Some Infinite Expansions of the Lauricella Functions and Their Application in the Study of Fundamental Solutions of a Singular Elliptic Equation 劳里切拉函数的一些无限展开及其在奇异椭圆方程基本解研究中的应用
IF 0.7 Q2 MATHEMATICS Pub Date : 2024-07-19 DOI: 10.1134/s1995080224600742
T. G. Ergashev, A. Hasanov, T. K. Yuldashev

Abstract

In this article, a new inverse pair of symbolic operators withthe multidimensional analogues is introduced. The properties ofinverse pair of symbolic operators with the multidimensionalanalogues are studied. Formulas for the infinite expansion ofmultiple Lauricella functions are established. The application ofsome expansions in studying the properties of fundamentalsolutions of singular elliptic equations is shown.

摘要 本文介绍了一种新的符号算子逆对与多维类比。研究了符号算子逆对与多维类似的性质。建立了多个劳里切拉函数的无限展开公式。展示了某些展开在研究奇异椭圆方程基本解性质中的应用。
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引用次数: 0
期刊
Lobachevskii Journal of Mathematics
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