Selection between proportional and stratified hazards models based on expected log-likelihood

The problem of selecting between semi-parametric and proportional hazards models is considered. We propose to make this choice based on the expectation of the log-likelihood (ELL) which can be estimated by the likelihood cross-validation (LCV) criterion. The criterion is used to choose an estimator in families of semi-parametric estimators defined by the penalized likelihood. A simulation study shows that the ELL criterion performs nearly as well in this problem as the optimal Kullback–Leibler criterion in term of Kullback–Leibler distance and that LCV performs reasonably well. The approach is applied to a model of age-specific risk of dementia as a function of sex and educational level from the data of a large cohort study.     

Analysis of crack formation in bonded lap joints using finite fracture mechanics on the basis of linear elasticity solutions.

In this work, crack formation and the corresponding failure load of bonded lap joints is analyzed. The analysis is based on linear elasticity solutions for bonded lap joints and makes use of the finite fracture mechanics. A hybrid criterion is applied that states the spontaneous formation of a crack of finite size if a stress and an energy criterion are fulfilled simultaneously. The stress distribution of a linear elasticity solution is used for the stress criterion and for the calculation of the incremental energy release rate which is necessary for definition of the energy criterion. The resulting fracture criterion is compared to literature results and shows a good agreement. (© 2011 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

JOINT MODEL AND CRITERION OPTIMAL EXPERIMENT DESIGN

In this paper,a new optimal design criterion--joint model and criterion optimal de-sign criterioon is put forward. The design that is subject to this criterion satisfies many kinds of lin-ear optimal criterion and D-optimal criterion on several experiment models at the same time. Theequivalent condition of this optimal design is given. Its iterative algorithm and the algorithm cover-genee are stated.     

H p multipliers on stratified groups

Summary In this paper we give a criterion for boundedness on the Hardy spaces for functions M() of the sublaplacian on a stratified group. The criterion requires that the function M satisfies locally a Besov condition. The proof is based on the atomic and molecular characterization of Hardy spaces.     

On Cycles on Compact Locally Symmetric Varieties

 We give a criterion to determine when the cycle class of a locally symmetric subvariety of a compact locally symmetric variety generates a non-trivial module under the action of Hecke operators, and give several examples where this criterion is satisfied. We also exhibit examples of subvarieties which do generate the trivial module under the action of Hecke operators. We show that all Hodge classes (in degree ) on the locally symmetric variety associated to certain arithmetric subgroups Γ of are algebraic (provided that ). Received 16 January 2001; in revised form 18 October 2001     

A note on packing paths in planar graphs

Seymour (1981) proved that the cut criterion is necessary and sufficient for the solvability of the edge-disjoint paths problem when the union of the supply graph and the demand graph is planar and Eulerian. When only planarity is required, Middendorf and Pfeiffer (1993) proved the problem to be NP-complete. For this case, Korach and Penn (1992) proved that the cut criterion is sufficient for the existence of a near-complete packing of paths. Here we generalize this result by showing how a natural strengthening of the cut criterion yields better packings of paths.Analogously to Seymour's approach, we actually prove a theorem on packing cuts in an arbitrary graph and then the planar edge-disjoint paths case is obtained by planar dualization. The main result is derived from a theorem of Seb (1990) on the structure of ±1 weightings of a bipartite graph with no negative circuits.Research partially supported by the Hungarian National Foundation for Scientific Research Grants OTKA 2118 and 4271.     

A note on p-curvatures

In this note, we give an arithmetic criterion for the Lie-irreducibility of linear differential equations based on p-curvatures.     

A perturbation theorem for positive contraction semigroups on L 1-spaces with applications to transport equations and Kolmogorov's differential equations

In this paper, a criterion is given for assuring that a linear positive contraction C ₀-semigroup defined on an L ¹-space is generated by the closure of A+B, A and B being suitable unbounded linear operators. Furthermore, this criterion is applied to the transport equation, Kolmogorov's differential equations, and a transport equation modelling cell growth.     

Subspace Lang conjecture and some remarks on a transcendental criterion

Let \(b\ge 2\) be an integer and \(\alpha \) is a non-zero real number written in b-ary expansion. Adamczewski et al. (C. R. Acad. Sci. Paris 339 (2004) 11–14) provided a criterion for an irrational number to be a transcendental number using b-ary expansion. In this paper, we make some remarks on this criterion and, under the assumption of Subspace Lang Conjecture, we extend this criterion for a much wider class of irrational numbers.     

on stability criterion of complete intersections

For protective varieties, it is known that Chow stable implies N-th Hilbert-Mumford stable for N sufficiently large, which follows from the works of J. Fogarty [2, 6]. In this article, we firstly shall provide a simple criterion for Chow stability of complete intersections. The criterion for Chow stability was previously provided by Mumford [5], but our calculation is different from Mumford’s in that ours is based on the results of Zhang’s article [10]. Applying it, we secondly shall give an elementary proof of the above implications in a complete intersections case.     

A Comparative Investigation on Model Selection in Independent Factor Analysis

With uncorrelated Gaussian factors extended to mutually independent factors beyond Gaussian, the conventional factor analysis is extended to what is recently called independent factor analysis. Typically, it is called binary factor analysis (BFA) when the factors are binary and called non-Gaussian factor analysis (NFA) when the factors are from real non-Gaussian distributions. A crucial issue in both BFA and NFA is the determination of the number of factors. In the literature of statistics, there are a number of model selection criteria that can be used for this purpose. Also, the Bayesian Ying-Yang (BYY) harmony learning provides a new principle for this purpose. This paper further investigates BYY harmony learning in comparison with existing typical criteria, including Akaik’s information criterion (AIC), the consistent Akaike’s information criterion (CAIC), the Bayesian inference criterion (BIC), and the cross-validation (CV) criterion on selection of the number of factors. This comparative study is made via experiments on the data sets with different sample sizes, data space dimensions, noise variances, and hidden factors numbers. Experiments have shown that for both BFA and NFA, in most cases BIC outperforms AIC, CAIC, and CV while the BYY criterion is either comparable with or better than BIC. In consideration of the fact that the selection by these criteria has to be implemented at the second stage based on a set of candidate models which have to be obtained at the first stage of parameter learning, while BYY harmony learning can provide not only a new class of criteria implemented in a similar way but also a new family of algorithms that perform parameter learning at the first stage with automated model selection, BYY harmony learning is more preferred since computing costs can be saved significantly.     

On a criterion for continuity and compactness of composition operators acting on α-Bloch spaces

In this Note we give a new criterion for the continuity and compactness of composition operators acting on α-Bloch spaces.     

Dynamical systems of translation groups on a torus

The criterion for linearizability is obtained by a property of denominator of rational numbers that are given by continued fractions. We can regard this criterion as a condition given by behaviors of orbits of dynamical systems of translation groups on a one-dimensional real torus. By using continued fractions, we obtain a criterion that is an analogous phenomenon in several complex variables that is determined by behaviors of dynamical systems of translation groups on a one-dimensional complex torus.     

A note on global stability of three-dimensional Ricker models

In the recent paper [E. C. Balreira, S. Elaydi, and R. Luís, J. Differ. Equ. Appl. 23 (2017), pp. 2037–2071], Balreira, Elaydi and Luís established a good criterion for competitive mappings to have a globally asymptotically stable interior fixed point by a geometric approach. This criterion can be applied to three dimensional Kolmogorov competitive mappings on a monotone region with a carrying simplex whose planar fixed points are saddles but globally asymptotically stable on their positive coordinate planes. For three dimensional Ricker models, they found mild conditions on parameters such that the criterion can be applied to. Observing that Balreira, Elaydi and Luís' discussion is still valid for the monotone region with piecewise smooth boundary, we prove in this note that the interior fixed point of three dimensional Kolmogorov competitive mappings is globally asymptotically stable if they admit a carrying simplex and three planar fixed points which are saddles but globally asymptotically stable on their positive coordinate planes. This result is much easier to apply in the application.     

Limit analysis and numerical modeling of spherically porous solids with Coulomb and Drucker-Prager matrices

The first goal of this work was to develop efficient limit analysis (la) tools to investigate the macroscopic criterion of a porous material on the basis of the hollow sphere model used by Gurson, here with a Coulomb matrix. Another goal was to give the resulting rigorous lower and upper bounds to the macroscopic criterion to enable comparisons and validations with further analytical or numerical studies on this micro-macro problem. In both static and kinematic approaches of la, a quadratic formulation was used to represent the stress and displacement velocity fields, in triangular finite elements. A significant improvement of the quality of the results was obtained by superimposing, on the fem fields, analytical fields which are the solutions to the problem under isotropic loadings.The final problems result in conic optimization, or linear programming after linearization of the criterion, so as to determine the “Porous Coulomb” criterion. A fine iterative post-analysis strictly restores the admissibility of the static and kinematic solutions. After presenting the results for various values of the porosity and internal friction angle, a comparison with a heuristic Cam-Clay-like criterion shows that this criterion cannot be considered a precise general approximation. Then a comparison with the “Porous Drucker-Prager” criterion treated by specific 3D codes is presented. With the same numerical tools, a final analysis of recent results in the literature is detailed, and tables of selected numerical data are presented in the appendices.     

Self-adjointness of Toeplitz operators on the Segal-Bargmann space

We prove a new criterion that guarantees self-adjointness of Toeplitz operators with unbounded operator-valued symbols. Our criterion applies, in particular, to symbols with Lipschitz continuous derivatives, which is the natural class of Hamiltonian functions for classical mechanics. For this we extend the Berger-Coburn estimate to the case of vector-valued Segal-Bargmann spaces. Finally, we apply our result to prove self-adjointness for a class of (operator-valued) quadratic forms on the space of Schwartz functions in the Schrödinger representation.     

Comparison of criteria on the direction of crack extension

There are three famous criteria for the prediction on the direction of crack extension: maximum energy release rate criterion, local symmetric criterion and maximum stress criterion. It has already been proved that these criteria are different. In this paper, we show how to measure the difference between maximum energy release rate criterion and maximum stress criterion. The results in this paper and special solutions in Amestoy and Leblond (Internat. J. Solids Struct. 29 (1992) 465) indicate that it is enough to use the maximum stress criterion for the numerical prediction of crack path, if the stress intensity factor of the shearing mode is not too big.     

Separability for Positive Operators on Tensor Product of Hilbert Spaces

The separability and the entanglement(that is, inseparability) of the composite quantum states play important roles in quantum information theory. Mathematically, a quantum state is a trace-class positive operator with trace one acting on a complex separable Hilbert space. In this paper,in more general frame, the notion of separability for quantum states is generalized to bounded positive operators acting on tensor product of Hilbert spaces. However, not like the quantum state case, there are different kinds of separability for positive operators with different operator topologies. Four types of such separability are discussed; several criteria such as the finite rank entanglement witness criterion,the positive elementary operator criterion and PPT criterion to detect the separability of the positive operators are established; some methods to construct separable positive operators by operator matrices are provided. These may also make us to understand the separability and entanglement of quantum states better, and may be applied to find new separable quantum states.     

Ned sets on a hyperplane

Under study are the sets in ℝ ⁿ (NED sets) each of which does not affect the conformal capacity of any condenser with connected plates disjoint from this set. These sets are removable singularities of quasiconformal mappings, which explains our interest in them. For compact sets on a hyperplane we obtain a geometric criterion of the NED property; we point out a simple sufficient condition for an NED set in terms of the connected attainability of its points from its complement in the hyperplane. For compact sets on a hypersphere we obtain a criterion for an NED set in terms of the reduced module at a pair of points in its complement. We establish that a compact set on a hypersphere S, removable for the capacity in at least one spherical ring concentric with S and containing S, is an NED set.     

Note on a theorem of A. Aiba

Recently A. Aiba (J. Number Theory 102 (2003) 118) gave a criterion whether the valuation ring of a wildly ramified Artin-Schreier extension of F_q((T)) is isomorphic to the associated order of this extension. We correct a mistake of (Aiba (2003)) and give easier substitutes for the (modified) condition of that criterion.