Communications in Mathematics and Statistics
Journal Prestige (SJR): 0.556 Citation Impact (citeScore): 1 Number of Followers: 3 Hybrid journal (It can contain Open Access articles) ISSN (Print) 21946701  ISSN (Online) 2194671X Published by SpringerVerlag [2467 journals] 
 Variable Selection for Distributed Sparse Regression Under Memory
Constraints
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Abstract: Abstract This paper studies variable selection using the penalized likelihood method for distributed sparse regression with large sample size n under a limited memory constraint. This is a much needed research problem to be solved in the big data era. A naive divideandconquer method solving this problem is to split the whole data into N parts and run each part on one of N machines, aggregate the results from all machines via averaging, and finally obtain the selected variables. However, it tends to select more noise variables, and the false discovery rate may not be well controlled. We improve it by a special designed weighted average in aggregation. Although the alternating direction method of multiplier can be used to deal with massive data in the literature, our proposed method reduces the computational burden a lot and performs better by mean square error in most cases. Theoretically, we establish asymptotic properties of the resulting estimators for the likelihood models with a diverging number of parameters. Under some regularity conditions, we establish oracle properties in the sense that our distributed estimator shares the same asymptotic efficiency as the estimator based on the full sample. Computationally, a distributed penalized likelihood algorithm is proposed to refine the results in the context of general likelihoods. Furthermore, the proposed method is evaluated by simulations and a real example.
PubDate: 20230201

 Relative TimeRestricted Sensitivity and Entropy

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Abstract: Abstract In this paper, we consider relativization of measuretheoretical restricted sensitivity. For a given topological dynamical system, we define conditional measuretheoreticalrestricted asymptotic rate with respect to sensitivity and obtain that it equals to the reciprocal of the Brin–Katok local entropy for almost every point under the conditional measure.
PubDate: 20230131

 Harnack Inequalities for GSDEs with Multiplicative Noise

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Abstract: Abstract The Harnack inequality for stochastic differential equation driven by GBrownian motion with multiplicative noise is derived by means of the coupling by change of measure, which extends the corresponding results derived in Wang (Probab. Theory Related Fields 109:417–424) under the linear expectation. Moreover, we generalize the gradient estimate under nonlinear expectation appeared in Song (Sci. China Math. 64:1093–1108).
PubDate: 20230131

 fHarmonic Maps Within Bounded Distance from Quasiisometric Maps

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Abstract: Abstract In this article, we prove that a quasiisometric map between rank one symmetric spaces is within bounded distance from an fharmonic map.
PubDate: 20230130

 Frobenius Manifolds and a New Class of Extended Affine Weyl Groups of
Atype (II)
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Abstract: Abstract With the help of the local isomorphism between the Hurwitz space \(M_{0;k1,lkr+1,r1}\) and the orbit space \(\mathcal {M}_{k,k+r}(A_l)\) , we will show the existence of a Frobenius manifold structure on the orbit space \(\mathcal {M}_{k,k+r}(A_l)\setminus \Sigma _r\) of the extended affine Weyl group \(\widetilde{W}^{(k,k+r)}(A_l)\) for \(1\le k<k+r\le l\) .
PubDate: 20230129

 The Number of Triangles in Random Intersection Graphs

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Abstract: Abstract Let \(T_n\) be the number of triangles in the random intersection graph G(n, m, p). When the mean of \(T_n\) is bounded, we obtain an upper bound on the total variation distance between \(T_n\) and a Poisson distribution. When the mean of \(T_n\) tends to infinity, the Stein–Tikhomirov method is used to bound the error for the normal approximation of \(T_n\) with respect to the Kolmogorov metric.
PubDate: 20230129

 Functional Shige Peng’s Central Limit Theorems for Martingale
Vectors
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Abstract: Abstract In this paper, the functional central limit theorem is established for martingale like random vectors under the framework sublinear expectations introduced by Shige Peng. As applications, the Lindeberg central limit theorem for independent random vectors is established, the sufficient and necessary conditions of the central limit theorem for independent and identically distributed random vectors are found, and a Lévy’s characterization of a multidimensional GBrownian motion is obtained.
PubDate: 20230120

 On $$\sigma $$ Solubility Criteria for Finite Groups

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Abstract: Abstract In this paper, the structure of finite groups in which maximal subgroups of some Sylow subgroups have a \(\sigma \) soluble or \(\sigma \) nilpotent supplement, where \(\sigma \) is a partition of the set of all prime numbers, is investigated. Some solubility, \(\sigma \) solubility and \(\sigma \) nilpotency criteria leading to some significant improvements of earlier results are given.
PubDate: 20230116

 Identification and Estimation of Generalized Additive Partial Linear
Models with Nonignorable Missing Response
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Abstract: Abstract The generalized additive partial linear models (GAPLM) have been widely used for flexible modeling of various types of response. In practice, missing data usually occurs in studies of economics, medicine, and public health. We address the problem of identifying and estimating GAPLM when the response variable is nonignorably missing. Three types of monotone missing data mechanism are assumed, including logistic model, probit model and complementary loglog model. In this situation, likelihood based on observed data may not be identifiable. In this article, we show that the parameters of interest are identifiable under very mild conditions, and then construct the estimators of the unknown parameters and unknown functions based on a likelihoodbased approach by expanding the unknown functions as a linear combination of polynomial spline functions. We establish asymptotic normality for the estimators of the parametric components. Simulation studies demonstrate that the proposed inference procedure performs well in many settings. We apply the proposed method to the household income dataset from the Chinese Household Income Project Survey 2013.
PubDate: 20230113

 Weak Solutions of McKean–Vlasov SDEs with Supercritical Drifts

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Abstract: Abstract Consider the following McKean–Vlasov SDE: $$\begin{aligned} \textrm{d} X_t=\sqrt{2}\textrm{d} W_t+\int _{{\mathbb {R}}^d}K(t,X_ty)\mu _{X_t}(\textrm{d} y)\textrm{d} t,\ \ X_0=x, \end{aligned}$$ where \(\mu _{X_t}\) stands for the distribution of \(X_t\) and \(K(t,x): {{\mathbb {R}}}_+\times {{\mathbb {R}}}^d\rightarrow {{\mathbb {R}}}^d\) is a timedependent divergence free vector field. Under the assumption \(K\in L^q_t({\widetilde{L}}_x^p)\) with \(\frac{d}{p}+\frac{2}{q}<2\) , where \({\widetilde{L}}^p_x\) stands for the localized \(L^p\) space, we show the existence of weak solutions to the above SDE. As an application, we provide a new proof for the existence of weak solutions to 2D Navier–Stokes equations with measure as initial vorticity.
PubDate: 20230112

 Floer Homology: From Generalized Morse–Smale Dynamical Systems to
Forman’s Combinatorial Vector Fields
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Abstract: Abstract We construct a Floer type boundary operator for generalised Morse–Smale dynamical systems on compact smooth manifolds by counting the number of suitable flow lines between closed (both homoclinic and periodic) orbits and isolated critical points. The same principle works for the discrete situation of general combinatorial vector fields, defined by Forman, on CW complexes. We can thus recover the \(\mathbb {Z}_2\) homology of both smooth and discrete structures directly from the flow lines (Vpaths) of our vector field.
PubDate: 20221227

 Katok’s Entropy Formula of Unstable Metric Entropy for Partially
Hyperbolic Diffeomorphisms
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Abstract: Abstract Katok’s entropy formula is an important formula in entropy theory. It plays significant roles in large deviation theories, multifractal analysis, quantitative recurrence and so on. This paper is devoted to establishing Katok’s entropy formula of unstable metric entropy which is the entropy caused by the unstable part of partially hyperbolic systems. We also construct a similar formula which can be used to study the quantitative recurrence in the unstable manifold for partially hyperbolic diffeomorphisms.
PubDate: 20221226

 Estimations of Bounds on the Multiplicative Fractional Integral
Inequalities Having Exponential Kernels
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Abstract: Abstract To investigate the fractional Hermite–Hadamardtype inequalities, a class of the multiplicative fractional integrals having exponential kernels is introduced. Some estimations of upper bounds for the newly introduced class of integral operators are obtained in terms of the established \(^*\) differentiable identity. And our results presented in this study are substantial generalizations of previous findings given by Ali et al. (Asian Res J Math 12:1–11, 2019). Three examples are also provided to identify the correctness of the results that occur with the change of the parameter \(\alpha \) .
PubDate: 20221224

 Power Generalized Weibull Distribution Based on Record Values and
Associated Inferences with Bladder Cancer Data Example
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Abstract: Abstract The power generalized Weibull distribution has been proposed recently by [24] as an alternative to the gamma, Weibull and the exponentiated Weibull distributions. The power generalized Weibull family is suitable for modeling data that indicate nonmonotone hazard rates and can be used in survival analysis and reliability studies. Usefulness and flexibility of the family are illustrated by reanalyzing Efron’s data pertaining to a headandneck cancer clinical trial. These data involve censoring and indicate unimodal hazard rate. For this distribution, some recurrence relations are established for the single and product moments of upper record values. Further, using these relations, we have obtained means, variances and covariances of upper record values from samples of sizes up to 10 for various values of the parameters and present them in figures. Real data set is analyzed to illustrate the flexibility and importance of the model.
PubDate: 20221223

 Livšic Theorem for Matrix Cocycles Over An Axiom A Flow

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Abstract: Abstract In this paper, we prove a version of Livšic theorem for a class of matrix cocycles over a \(C^2\) Axiom A flow. As a byproduct, an approximative theorem on Lyapunov exponents is also obtained which assets that Lyapunov exponents of a given ergodic measure can be approximated by those of periodic measures.
PubDate: 20221201
DOI: 10.1007/s4030402100250x

 A HighDimensional Test for Multivariate Analysis of Variance Under a
LowDimensional Factor Structure
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Abstract: Abstract In this paper, the problem of highdimensional multivariate analysis of variance is investigated under a lowdimensional factor structure which violates some vital assumptions on covariance matrix in some existing literature. We propose a new test and derive that the asymptotic distribution of the test statistic is a weighted distribution of chisquares of 1 degree of freedom under the null hypothesis and mild conditions. We provide numerical studies on both sizes and powers to illustrate performance of the proposed test.
PubDate: 20221201
DOI: 10.1007/s40304020002361

 Designing Optimal Large FourLevel Experiments: A New Technique Without
Recourse to Optimization Softwares
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Abstract: Abstract Experimental design is an effective statistical tool that is extensively applied in modern industry, engineering, and science. It is proved that experimental design is a powerful and efficient means to screen the relationships between input factors and their responses, and to distinguish significant and unimportant factor effects. In many practical situations, experimenters are faced with large experiments having fourlevel factors. Even though there are several techniques provided to design such experiments, the challenge faced by the experimenters is still daunting. The practice has demonstrated that the existing techniques are highly timeconsuming optimization procedures, satisfactory outcomes are not guaranteed, and nonmathematicians face a significant challenge in dealing with them. A new technique that can overcome these defects of the existing techniques is presented in this paper. The results demonstrated that the proposed technique outperformed the current techniques in terms of construction simplicity, computational efficiency and achieving satisfactory results capability. For nonmathematician experimenters, the new technique is much easier and simpler than the current techniques, as it allows them to design optimal large experiments without the recourse to optimization softwares. The optimality is discussed from four basic perspectives: maximizing the dissimilarity among experimental runs, maximizing the number of independent factors, minimizing the confounding among factors, and filling the experimental domain uniformly with as few gaps as possible.
PubDate: 20221201
DOI: 10.1007/s4030402100241y

 Rigid Analytic pAdic Simpson Correspondence for Line Bundles

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Abstract: Abstract The padic Simpson correspondence due to Faltings (Adv Math 198(2):847–862, 2005) is a padic analogue of nonabelian Hodge theory. The following is the main result of this article: The correspondence for line bundles can be enhanced to a rigid analytic morphism of moduli spaces under certain smallness conditions. In the complex setting, Simpson shows that there is a complex analytic morphism from the moduli space for the vector bundles with integrable connection to the moduli space of representations of a finitely generated group as algebraic varieties. We give a padic analogue of Simpson’s result.
PubDate: 20221201
DOI: 10.1007/s40304021002565

 DistanceRegular Graphs of Diameter 3 Without Triangles with $$c_2=2$$

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Abstract: Abstract Earlier it was proved that some distanceregular graphs of diameter 3 with \(c_2=2\) do not exist. Distanceregular graph \(\varGamma \) with intersection array \(\{17,16,10;1,2,8\}\) has strongly regular graph \(\varGamma _{3}\) (pseudogeometric graph for the net \(pG_9(17,9)\) ). By symmetrizing the arrays of triple intersection numbers, it is proved that the distanceregular graphs with intersection arrays \(\{17,16,10;1,2,8\}\) and \(\{22,21,4;1,2,14\}\) do not exist.
PubDate: 20221002
DOI: 10.1007/s40304021002814

 Tool Orientation Optimization Based on Spatial Tractrix Method for
FiveAxis CNC Machining with Ball End Cutters
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Abstract: Abstract When milling part surfaces with a ballend tool in 5axis CNC machining, maintaining a constant cutting speed by keeping a fixed inclination angle between the tool axis and surface normal is crucial to ensure safe operation and achieve high quality of the machined surface. Under this constraint, the variation of tool orientation is expected to be “smoothest possible” to reduce the angular speed of the rotary axes for the efficient and robust machining. To address this issue, the spatial tractrix which is the extension of classic tractrix is presented to establish the geometry model of the tool orientation kinematics in the part coordinate system. The proposed model describes the relations between the tilt angle and the variation of ballend tool orientation. Two spatial tractrixbased methods, synchronizing tractrixbased method and equilibrating tractrixbased method, are developed to minimize the variation of tool orientation by controlling the variation of tilt angle. These methods are used to plan the tool orientation on a part surface modeled by a bicubic spline surface. The performance evaluation carried by intense simulations demonstrates the equilibrating tractrixbased method provide the best results in most cases compared with the existing differential geometrybased methods such as the tractrixbased method and parallel transport method. The synchronizing tractrixbased method works well in some special cases.
PubDate: 20220915
DOI: 10.1007/s40304021002556
