Common Factor Cause-Specific Mortality Model

Recent pension reforms in Europe have implemented a link between retirement age and life expectancy. The accurate forecast of life tables and life expectancy is hence paramount for governmental policy and financial institutions. We developed a multi-population mortality model which includes a cause-specific environment using Archimedean copulae to model dependence between various groups of causes of death. For this, Dutch data on cause-of-death mortality and cause-specific mortality data from 14 comparable European countries were used. We find that the inclusion of a common factor to a cause-specific mortality context increases the robustness of the forecast and we underline that cause-specific mortality forecasts foresee a more pessimistic mortality future than general mortality models. Overall, we find that this non-trivial extension is robust to the copula specification for commonly chosen dependence parameters.

Forecasting intermittent and sparse time series: A unified probabilistic framework via deep renewal processes

Intermittency are a common and challenging problem in demand forecasting. We introduce a new, unified framework for building probabilistic forecasting models for intermittent demand time series, which incorporates and allows to generalize existing methods in several directions. Our framework is based on extensions of well-established model-based methods to discrete-time renewal processes, which can parsimoniously account for patterns such as aging, clustering and quasi-periodicity in demand arrivals. The connection to discrete-time renewal processes allows not only for a principled extension of Croston-type models, but additionally for a natural inclusion of neural network based models—by replacing exponential smoothing with a recurrent neural network. We also demonstrate that modeling continuous-time demand arrivals, i.e., with a temporal point process, is possible via a trivial extension of our framework. This leads to more flexible modeling in scenarios where data of individual purchase orders are directly available with granular timestamps. Complementing this theoretical advancement, we demonstrate the efficacy of our framework for forecasting practice via an extensive empirical study on standard intermittent demand data sets, in which we report predictive accuracy in a variety of scenarios.

Local dimension of trivial extension and amalgamation of rings

Local dimension is an ordinal valued invariant that is in some sense a measure of how far a ring is from being local and denoted [Formula: see text]. The purpose of this paper is to study the local dimension of ring extensions such as homomorphic image, trivial ring extension and the amalgamation of rings.

Korovkin type approximation via statistical e-convergence on two dimensional weighted spaces

In the present work, we prove a Korovkin theorem for statistical e-convergence on two dimensional weighted spaces. We show that our theorem is a non-trivial extension of some well-known Korovkin type approximation theorems. We also study the rate of statistical e-convergence by using the weighted modulus of continuity and afterwards we present an application in support of our result.

K-Groups of Trivial Extensions and Gluings of Abelian Categories

This paper focuses on the Ki-groups of two types of extensions of abelian categories, which are the trivial extension and the gluing of abelian categories. We prove that, under some conditions, Ki-groups of a certian subcategory of the trivial extension category is isomorphic to Ki-groups of the similar subcategory of the original category. Moreover, under some conditions, we show that the Ki-groups of a left (right) gluing of two abelian categories are isomorphic to the direct sum of Ki-groups of two abelian categories. As their applications, we obtain some results of the Ki-groups of the trivial extension of a ring by a bimodule (i∈N).

The rate of convergence on fractional power dissipative operator on compact manifolds

On a compact connected manifold M $\mathbb{M}$ , we concern the fractional power dissipative operator e − t L α $e^{-t\left\vert \mathcal{L}\right\vert ^{\alpha}}$ , and obtain the almost-everywhere convergence rate (as t → 0+) of e − t L α f $e^{-t\left\vert \mathcal{L}\right\vert ^{\alpha}}\left( f\right)$ when f is in some Sobolev type Hardy spaces. The main result is a non-trivial extension of a recent result on ℝ n by Cao and Wang in 2.

Unconstrained submodular maximization with modular costs

Given a set V , the problem of unconstrained submodular maximization with modular costs (USM-MC) asks for a subset S ⊆ V that maximizes f ( S ) - c ( S ), where f is a non-negative, monotone, and submodular function that gauges the utility of S , and c is a non-negative and modular function that measures the cost of S. This problem finds applications in numerous practical scenarios, such as profit maximization in viral marketing on social media. This paper presents ROI-Greedy, a polynomial time algorithm for USM-MC that returns a solution S satisfying [EQUATION], where S * is the optimal solution to USM-MC. To our knowledge, ROI-Greedy is the first algorithm that provides such a strong approximation guarantee. In addition, we show that this worst-case guarantee is tight , in the sense that no polynomial time algorithm can ensure [EQUATION], for any ϵ > 0. Further, we devise a non-trivial extension of ROI-Greedy to solve the profit maximization problem, where the precise value of f ( S ) for any set S is unknown and can only be approximated via sampling. Extensive experiments on benchmark datasets demonstrate that ROI-Greedy significantly outperforms competing methods in terms of the tradeoff between efficiency and solution quality.

System Z for Conditional Belief Bases with Positive and Negative Information

In non-monotonic reasoning, conditional belief bases mostly contain positive information in the form of standard conditionals. However, in practice we are often confronted with negative information, stating that a conditional does \emph{not} hold, i.e. we need a suitable approach for reasoning over belief bases $\Delta$ with positive and negative information. In this paper, we investigate the interaction of positive and negative information in a conditional belief base and establish a property for partitions of $\Delta$ that is equivalent to consistency. Based on this property, we develop a non-trivial extension of system Z for mixed conditional belief bases and provide an algorithm to compute this partition.