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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
Lobachevskii Journal of Mathematics Pub Date : 2024-07-19 DOI: 10.1134/s1995080224600766
M. L. Zymbler, A. I. Goglachev
{"title":"PaSTiLa: Scalable Parallel Algorithm for Unsupervised Labeling of Long Time Series","authors":"M. L. Zymbler, A. I. Goglachev","doi":"10.1134/s1995080224600766","DOIUrl":"https://doi.org/10.1134/s1995080224600766","url":null,"abstract":"<h3 data-test=\"abstract-sub-heading\">Abstract</h3><p>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 (<u>Pa</u>rallel <u>S</u>nippet-based <u>Ti</u>me series <u>La</u>beling) 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 <span>(textrm{F}_{1})</span> 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.</p>","PeriodicalId":46135,"journal":{"name":"Lobachevskii Journal of Mathematics","volume":null,"pages":null},"PeriodicalIF":0.7,"publicationDate":"2024-07-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141743890","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
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
Lobachevskii Journal of Mathematics Pub Date : 2024-07-19 DOI: 10.1134/s1995080224600572
B. D. Coulibaly, G. Chaibi, M. El Khomssi
{"title":"Statistical Modeling of the Cobb–Douglas Production Function: A Multiple Linear Regression Approach in Presence of Stable Distribution Noise","authors":"B. D. Coulibaly, G. Chaibi, M. El Khomssi","doi":"10.1134/s1995080224600572","DOIUrl":"https://doi.org/10.1134/s1995080224600572","url":null,"abstract":"<h3 data-test=\"abstract-sub-heading\">Abstract</h3><p>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 <span>(alpha)</span>-stable distribution. By adapting the traditional multiple linear regression model, our approach incorporates the <span>(alpha)</span>-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.</p>","PeriodicalId":46135,"journal":{"name":"Lobachevskii Journal of Mathematics","volume":null,"pages":null},"PeriodicalIF":0.7,"publicationDate":"2024-07-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141743896","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
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
Lobachevskii Journal of Mathematics Pub Date : 2024-07-19 DOI: 10.1134/s199508022460078x
A. N. Abdullozhonova, T. K. Yuldashev, A. K. Fayziyev
{"title":"Mixed Problem for an Impulsive Parabolic Integro-Differential Equation with Involution and Nonlinear Conditions","authors":"A. N. Abdullozhonova, T. K. Yuldashev, A. K. Fayziyev","doi":"10.1134/s199508022460078x","DOIUrl":"https://doi.org/10.1134/s199508022460078x","url":null,"abstract":"<h3 data-test=\"abstract-sub-heading\">Abstract</h3><p>In this paper, we consider an impulsive homogeneous parabolic\u0000type partial integro-differential equation with degenerate kernel\u0000and involution. With respect to spatial variable <span>(x)</span> is used\u0000Dirichlet boundary value conditions and spectral problem is\u0000studied. The Fourier method of separation of variables is applied.\u0000The countable system of nonlinear functional equations is obtained\u0000with respect to the Fourier coefficients of unknown function.\u0000Theorem on a unique solvability of countable system of functional\u0000equations is proved. The method of successive approximations is\u0000used in combination with the method of contraction mapping. The\u0000unique solution of the impulsive mixed problem is obtained in the\u0000form of Fourier series. Absolutely and uniformly convergence of\u0000Fourier series is proved.</p>","PeriodicalId":46135,"journal":{"name":"Lobachevskii Journal of Mathematics","volume":null,"pages":null},"PeriodicalIF":0.7,"publicationDate":"2024-07-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141746451","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
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
Lobachevskii Journal of 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
{"title":"Some Aspects of Remote State Restoring in State Transfer Governed by XXZ-Hamiltonian","authors":"G. A. Bochkin, S. I. Doronin, E. B. Fel’dman, E. I. Kuznetsova, I. D. Lazarev, A. N. Pechen, A. I. Zenchuk","doi":"10.1134/s1995080224600596","DOIUrl":"https://doi.org/10.1134/s1995080224600596","url":null,"abstract":"<h3 data-test=\"abstract-sub-heading\">Abstract</h3><p>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.</p>","PeriodicalId":46135,"journal":{"name":"Lobachevskii Journal of Mathematics","volume":null,"pages":null},"PeriodicalIF":0.7,"publicationDate":"2024-07-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141743894","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
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
Lobachevskii Journal of Mathematics Pub Date : 2024-07-19 DOI: 10.1134/s1995080224600808
Kh. T. Dekhkonov, Yu. E. Fayziev, R. R. Ashurov
{"title":"On the Non-local Problem for a Boussinesq Type Equations","authors":"Kh. T. Dekhkonov, Yu. E. Fayziev, R. R. Ashurov","doi":"10.1134/s1995080224600808","DOIUrl":"https://doi.org/10.1134/s1995080224600808","url":null,"abstract":"<h3 data-test=\"abstract-sub-heading\">Abstract</h3><p>The problem of finding a solution, satisfying the non-local condition <span>(u(xi_{0})=alpha u(+0)+varphi)</span> in time for the Boussinesq type equation of the form <span>(u_{tt}+Au_{tt}+Au=f)</span> is studied in the article. Here <span>(alpha)</span> and <span>(xi_{0})</span>, <span>(xi_{0}in(0,T],)</span> are the given numbers, <span>(A:Hrightarrow H)</span> is the self-adjoint, unbounded, positive operator defined in the Hilbert separable space <span>(H)</span>. By using the Fourier method, it was shown that the solution to the problem exists and is unique. The effect of parameter <span>(alpha)</span> 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.</p>","PeriodicalId":46135,"journal":{"name":"Lobachevskii Journal of Mathematics","volume":null,"pages":null},"PeriodicalIF":0.7,"publicationDate":"2024-07-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141743897","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
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
Lobachevskii Journal of Mathematics Pub Date : 2024-07-19 DOI: 10.1134/s1995080224600857
D. K. Durdiev, M. Akylbayev, Zh. Maxumova, A. Iskakova
{"title":"A 2D Convolution Kernel Determination Problem for the Time-Fractional Diffusion Equation","authors":"D. K. Durdiev, M. Akylbayev, Zh. Maxumova, A. Iskakova","doi":"10.1134/s1995080224600857","DOIUrl":"https://doi.org/10.1134/s1995080224600857","url":null,"abstract":"<h3 data-test=\"abstract-sub-heading\">Abstract</h3><p>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.</p>","PeriodicalId":46135,"journal":{"name":"Lobachevskii Journal of Mathematics","volume":null,"pages":null},"PeriodicalIF":0.7,"publicationDate":"2024-07-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141743899","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
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 $$mu$ - 值
IF 0.7
Lobachevskii Journal of Mathematics Pub Date : 2024-07-19 DOI: 10.1134/s1995080224600754
Mutti-Ur Rehman, Tulkin H. Rasulov, Fouzia Amir
{"title":"D-Stability, Strong D-Stability and $$mu$$ -Values","authors":"Mutti-Ur Rehman, Tulkin H. Rasulov, Fouzia Amir","doi":"10.1134/s1995080224600754","DOIUrl":"https://doi.org/10.1134/s1995080224600754","url":null,"abstract":"<h3 data-test=\"abstract-sub-heading\">Abstract</h3><p>In this article, we present some connections between the notation of D-stability, Strong D-stability, and structured singular values known as <span>(mu)</span>-values for square matrices.</p>","PeriodicalId":46135,"journal":{"name":"Lobachevskii Journal of Mathematics","volume":null,"pages":null},"PeriodicalIF":0.7,"publicationDate":"2024-07-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141743921","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
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
Lobachevskii Journal of Mathematics Pub Date : 2024-07-19 DOI: 10.1134/s1995080224600845
D. A. Tursunov, A. S. Sadieva, K. G. Kozhobekov, E. A. Tursunov
{"title":"Asymptotics of the Solution of the Cauchy Problem with an Unstable Spectrum and Prolonging Loss of Stability","authors":"D. A. Tursunov, A. S. Sadieva, K. G. Kozhobekov, E. A. Tursunov","doi":"10.1134/s1995080224600845","DOIUrl":"https://doi.org/10.1134/s1995080224600845","url":null,"abstract":"<h3 data-test=\"abstract-sub-heading\">Abstract</h3><p>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.</p>","PeriodicalId":46135,"journal":{"name":"Lobachevskii Journal of Mathematics","volume":null,"pages":null},"PeriodicalIF":0.7,"publicationDate":"2024-07-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141743889","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
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
Lobachevskii Journal of Mathematics Pub Date : 2024-07-19 DOI: 10.1134/s1995080224600547
B. Y. Ashirbaev, T. K. Yuldashev
{"title":"Derivation of a Controllability Criteria for a Linear Singularly Perturbed Discrete System with Small Step","authors":"B. Y. Ashirbaev, T. K. Yuldashev","doi":"10.1134/s1995080224600547","DOIUrl":"https://doi.org/10.1134/s1995080224600547","url":null,"abstract":"<h3 data-test=\"abstract-sub-heading\">Abstract</h3><p>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.</p>","PeriodicalId":46135,"journal":{"name":"Lobachevskii Journal of Mathematics","volume":null,"pages":null},"PeriodicalIF":0.7,"publicationDate":"2024-07-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141743893","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
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
Lobachevskii Journal of Mathematics Pub Date : 2024-07-19 DOI: 10.1134/s1995080224600742
T. G. Ergashev, A. Hasanov, T. K. Yuldashev
{"title":"Some Infinite Expansions of the Lauricella Functions and Their Application in the Study of Fundamental Solutions of a Singular Elliptic Equation","authors":"T. G. Ergashev, A. Hasanov, T. K. Yuldashev","doi":"10.1134/s1995080224600742","DOIUrl":"https://doi.org/10.1134/s1995080224600742","url":null,"abstract":"<h3 data-test=\"abstract-sub-heading\">Abstract</h3><p>In this article, a new inverse pair of symbolic operators with\u0000the multidimensional analogues is introduced. The properties of\u0000inverse pair of symbolic operators with the multidimensional\u0000analogues are studied. Formulas for the infinite expansion of\u0000multiple Lauricella functions are established. The application of\u0000some expansions in studying the properties of fundamental\u0000solutions of singular elliptic equations is shown.</p>","PeriodicalId":46135,"journal":{"name":"Lobachevskii Journal of Mathematics","volume":null,"pages":null},"PeriodicalIF":0.7,"publicationDate":"2024-07-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141743912","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
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