Bivariate Density Estimation with an Application to Survival Analysis

Abstract

A procedure for estimating a bivariate density based on data that may be censored is described. After the data are transformed to the unit square, the bivariate density is estimated using linear splines and their tensor products. The combined procedure yields an estimate of the bivariate density on the original scale, which may provide insight about the dependence structure. The procedure can also be used to estimate densities that are known to be symmetric and to test for independence.     

Improved hidden vector encryption with short ciphertexts and tokens

Hidden vector encryption (HVE) is a particular kind of predicate encryption that is an important cryptographic primitive having many applications, and it provides conjunctive equality, subset, and comparison queries on encrypted data. In predicate encryption, a ciphertext is associated with attributes and a token corresponds to a predicate. The token that corresponds to a predicate f can decrypt the ciphertext associated with attributes x if and only if f(x) = 1. Currently, several HVE schemes were proposed where the ciphertext size, the token size, and the decryption cost are proportional to the number of attributes in the ciphertext. In this paper, we construct efficient HVE schemes where the token consists of just four group elements and the decryption only requires four bilinear map computations, independent of the number of attributes in the ciphertext. We first construct an HVE scheme in composite order bilinear groups and prove its selective security under the well-known assumptions. Next, we convert it to use prime order asymmetric bilinear groups where there are no efficiently computable isomorphisms between two groups.     

Random attractors for stochastic differential equations driven by two-sided Lévy processes

Abstract

In this paper, the asymptotic behavior of solutions for a nonlinear Marcus stochastic differential equation with multiplicative two-sided Lévy noise is studied. We plan to consider this equation as a random dynamical system. Thus, we have to interpret a Lévy noise as a two-sided metric dynamical system. For that, we have to introduce some fundamental properties of such a noise. So far most studies have only discussed two-sided Lévy processes which are defined by combining two-independent Lévy processes. In this paper, we use another definition of two-sided Lévy process by expanding the probability space. Having this metric dynamical system we will show that the Marcus stochastic differential equation with a particular drift coefficient and multiplicative noise generates a random dynamical system which has a random attractor.     

Analysis of some bivariate non-linear interpolatory subdivision schemes

This paper is devoted to the convergence analysis of a class of bivariate subdivision schemes that can be defined as a specific perturbation of a linear subdivision scheme. We study successively the univariate and bivariate case and apply the analysis to the so called Powerp scheme (Serna and Marquina, J Comput Phys 194:632–658, 2004).     

Mod-retractable strongly π-regular rings and group algebras

Abstract

In this work, we show that a two-sided mod-retractable and strongly π-regular ring is two-sided semiartinian. On the other hand, a strongly π-regular von Neumann regular ring is left mod-retractable if and only if it is a left semiartinian V-ring. We apply these results to group algebras and thereby we give the complete structure of groups whose group algebras are mod-retractable.

Communicated by Toma Albu     

The scale of a quasi-uniform space

We investigate the left-sided scale and the two-sided scale of a quasi-uniform space. While the two-sided scale of a quasi-uniform space X shows a behavior similar to the usual hyperspace of X equipped with its Hausdorff quasiuniformity, the left-sided scale generalizes the quasi-uniform multifunction space of X into itself.     

Optical fibre sensors for assessing food quality in full scale production ovens — a principal component analysis and artificial neural network based approach

This paper reports on a method of classifying the spectral data from an optical fibre based sensor system as used in the food processing industry for monitoring food products as they are cooked in large scale continuous ovens. The method uses a feed-forward back-propagation artificial neural network. The sensor monitors the food colour online as the product cooks by examining the reflected light, in the visible region, from both the surface and the core of the product. Results based on the combined use of Principal Component Analysis (PCA) and standard back-propagation artificial neural networks are presented. Results are also reported for a wide range of food products which have been cooked in the full scale industrial oven. PCA is performed on the reflected spectra, which form a “colour scale” — a scale developed to allow the quality of several products of similar colour to be monitored, i.e. a single classifier is trained, using the colour scale data, that can classify several food products. The results presented show that the classifier performs well.     

A comparative study on the co-existing attractors in the Gaussian map and its q-deformed version

In a recent study Jaganathan and Sinha [Jaganathan R, Sinha S. A q-deformed nonlinear map. Phys Lett A 2005;338:277–87] have introduced a scheme for the q-deformation of nonlinear maps using the logistic map as an example and shown that the q-logistic map exhibits a wide spectrum of dynamical behaviours including the co-existence of attractors (which is a rare phenomenon in one-dimensional maps). In this paper, we aim to analyze another famous one-dimensional map – the Gaussian map (a known one-dimensional map exhibiting co-existing attractors) subject to the same q-deformation scheme. We compare the dynamical behaviour of the Gaussian map and q-deformed Gaussian map with a special attention on the regions of the parameter space, where these maps exhibit co-existing attractors. An important conclusion of the present study is that the appearance of co-existing attractors for a particular choice of system parameters can be understood as a consequence of the presence of multiple fixed points in one-dimensional nonlinear maps; however the converse is not always true.     

Two-Sided Approximation of Solutions of Boundary-Value Problems

We propose a general scheme for the two-sided approximation of solutions of boundary-value problems for ordinary differential equations. This scheme involves a number of known and new two-sided methods. In our investigation, we use constructions of the Samoilenko numerical-analytic method together with the procedure of the construction of two-sided methods proposed by Kurpel’ and Shuvar.__________Translated from Ukrains’kyi Matematychnyi Zhurnal, Vol. 57, No. 2, pp. 284–288, February, 2005.     

Inner-product encryption under standard assumptions

Predicate encryption is a generalized notion for public key encryption that enables one to encrypt attributes as well as a message. In this paper, we present a new inner-product encryption (IPE) scheme, as a specialized predicate encryption scheme, whose security relies on the well-known Decision Bilinear Diffie-Hellman (BDH) and Decision Linear assumptions. Our IPE scheme uses prime order groups equipped with a bilinear map and works in both symmetric and asymmetric bilinear maps. Our result is the first construction of IPE under the standard assumptions. Prior to our work, all IPE schemes known to date require non-standard assumptions to prove security, and moreover some of them use composite-order groups. To achieve our goal, we introduce a novel technique for attribute-hiding, which may be of independent interest.     

A Fast and Stable Updating Algorithm for Bivariate Nonparametric Curve Estimation

Abstract

An updating algorithm for bivariate local linear regression is proposed. Thereby, we assume a rectangular design and a polynomial kernel constrained to rectangular support as weight function. Results of univariate regression estimators are extended to the bivariate setting. The updates are performed in a way that most of the well-known numerical instabilities of a naive update implementation can be avoided. Some simulation results illustrate the properties of several algorithms with respect to computing time and numerical stability.     

Topologies related to the prox map and the restricted center map

In this paper we review some of the recently introduced hypertopologies on collections of nonempty closed subsets of a metrizable space in the context of continuity properties of the prox map and the restricted center map. We identify here suitable families A, B of nonempty closed sets equipped with natural topologies, as coordinate spaces for the gap functional and the restricted radius functional, with a view to explore bivariate continuity of these functionals. This leads us to sharpenings of many known results as well as to some new results for upper semicontinuity of the prox map and the restricted center map. This, in turn, also leads us to improvements of certain best approximation results for convex-valued multifunctions and fixed point theorems for such multifunctions.     

Bivariate interpolation based on univariate subdivision schemes

The paper presents a bivariate subdivision scheme interpolating data consisting of univariate functions along equidistant parallel lines by repeated refinements. This method can be applied to the construction of a surface passing through a given set of parametric curves. Following the methodology of polysplines and tension surfaces, we define a local interpolator of four consecutive univariate functions, from which we sample a univariate function at the mid-point. This refinement step is the basis to an extension of the 4-point subdivision scheme to our setting. The bivariate subdivision scheme can be reduced to a countable number of univariate, interpolatory, non-stationary subdivision schemes. Properties of the generated interpolant are derived, such as continuity, smoothness and approximation order.     

Two-sided M-Bayesian credible limits of reliability parameters in the case of zero-failure data for exponential distribution

In this paper, we study the interval estimation of failure rate and reliability for exponential distribution, in the case of zero-failure data, using the method of two-sided Modified Bayesian (M-Bayesian) credible limit. We discuss the properties of two-sided M-Bayesian credible limits which include the impact of the value of upper bound c of hyper parameter, and the influence of different prior distributions of hyper parameter on two-sided M-Bayesian credible limits. The paper obtains the relationship between three kinds of two-sided M-Bayesian credible limits and two-sided classical confidence limits. Finally, we use a real data set to verify the properties of two-sided M-Bayesian credible limits, and the computing results indicate that the method is efficient and easy to operate.     

Alternative Superalgebras with DCC on Two-Sided Ideals#

We study the structure of alternative superalgebras that satisfy the descending chain condition (DCC) for two-sided ideals. The main results state that the Baer radical in an alternative superalgebra of characteristic ≠ 2, 3 with DCC on two-sided ideals is solvable and every such a semiprime superalgebra (of arbitrary characteristic) is isomorphic to a subdirect sum of an associative superalgebra with this property and a finite direct sum of simple alternative non-associative superalgebras.     

Three-colourings of planar 4-valent maps

A strong face 3-colouring of a planar 4-valent map G is a 3-colouring of the faces such that there is a face of each colour at every vertex. Such a map is one-track if it contains an Eulerian path which at each vertex regarded as a cross-roads goes directly through. It is proved that every planar 4-valent map can be strongly face 3-coloured and this can be done in a unique way if and only if G is one-track. Formulas are obtained for the number of strong face 3-colourings and the number of all face 3-colourings.     

Privacy-preserving data splitting: a combinatorial approach

Privacy-preserving data splitting is a technique that aims to protect data privacy by storing different fragments of data in different locations. In this work we give a new combinatorial formulation to the data splitting problem. We see the data splitting problem as a purely combinatorial problem, in which we have to split data attributes into different fragments in a way that satisfies certain combinatorial properties derived from processing and privacy constraints. Using this formulation, we develop new combinatorial and algebraic techniques to obtain solutions to the data splitting problem. We present an algebraic method which builds an optimal data splitting solution by using Gröbner bases. Since this method is not efficient in general, we also develop a greedy algorithm for finding solutions that are not necessarily minimally sized.

     

Trace- and pseudo-products: restriction-like semigroups with a band of projections

We ascertain conditions and structures on categories and semigroups which admit the construction of pseudo-products and trace products respectively, making their connection as precise as possible. This topic is modelled on the ESN Theorem and its generalisation to ample semigroups. Unlike some other variants of ESN, it is self-dual (two-sided), and the condition of commuting projections is relaxed. The condition that projections form a band (are closed under multiplication) is shown to be a very natural one. One-sided reducts are considered, and compared to (generalised) D-semigroups. Finally the special case when the category is a groupoid is examined.

     

基于三角直觉模糊数信息的双边匹配决策

本文研究了基于三角直觉模糊数信息的双边匹配问题。给出了三角直觉模糊数和双边匹配的相关理论;以实现每个主体三角直觉模糊满意度最高为目标,考虑到一对一双边匹配约束,构建了多目标双边匹配模型;运用线性加权法和三角模糊数重心法,将多目标双边匹配模型转化为单目标双边匹配模型;进而通过求解该模型获得“最佳”双边匹配方案。风险投资者和风险投资企业的匹配算例证明了所提双边匹配决策的可行性和实用性。     

Unconditionally-secure key pre-distribution for triangular grid based wireless sensor network

We present an unconditionally-secure key pre-distribution scheme for a wireless sensor network using t-degree bivariate polynomials. The proposed scheme is proven to be perfectly resilient against both node disconnection and link failure. The memory requirements, computation and communication overheads of our scheme are also favorable. Our scheme demonstrates superior performance compared to the existing similar schemes.