More on pooling spaces

A pooling space is a ranked poset P such that the subposet w⁺ induced by the elements above w is atomic for each element w of P. Pooling spaces were introduced in [T. Huang, C. Weng, Pooling spaces and non-adaptive pooling designs, Discrete Math. 282 (2004) 163-169] for the purpose of giving a uniform way to construct pooling designs, which have applications to the screening of DNA sequences. Many examples of pooling spaces were given in that paper. In this paper, we clarify a few things about the definition of pooling spaces. Then we find that a geometric lattice, a well-studied structure in literature, is also a pooling space. This provides us many classes of pooling designs, some old and some new. We study the pooling designs constructed from affine geometries. We find that some of them meet the optimal bounds related to a conjecture of Erdös, Frankl and Füredi.     

The fundamental theorem of mutual insurance

The essence of mutual insurance is the notion that re-distributing risk in a pool of risks is more beneficial than taking the risk alone. Interpreting ‘more beneficial’ as an increase in utility and considering sequences of exchangeable risks, we are able to formalize this notion from the policyholder’s perspective and demonstrate its validity for various alternative preference functionals (e.g., expected utility, Choquet expected utility, and distortion risk measures). To obtain this result, we exploit that for a sequence of exchangeable risks the corresponding sequence of arithmetical averages is a reversed martingale.We conclude that pooling risks is fundamental for understanding the mechanisms of insurance because it favourably affects the utility of policyholders, and we refer to this phenomenon as the ‘utility-improving effect of risk pooling’. Moreover, we demonstrate that the utility of the policyholder is (strictly) increasing with the size of the risk pool.     

Securitizing and tranching longevity exposures

We consider the problem of optimally designing longevity risk transfers under asymmetric information. We focus on holders of longevity exposures that have superior knowledge of the underlying demographic risks, but are willing to take them off their balance sheets because of capital requirements. In equilibrium, they transfer longevity risk to uninformed agents at a cost, where the cost is represented by retention of part of the exposure and/or by a risk premium. We use a signalling model to quantify the effects of asymmetric information and emphasize how they compound with parameter uncertainty. We show how the cost of private information can be minimized by suitably tranching securitized cashflows, or, equivalently, by securitizing the exposure in exchange for an option on mortality rates. We also investigate the benefits of pooling several longevity exposures and the impact on tranching levels.     

Spatially constrained sparse coding scheme for natural scene categorization

Coding and pooling, the major two sequential procedures in sparse coding based scene categorization systems, have drawn much attention in recent years. Yet improvements have been made for coding or pooling separately, this paper proposes a spatially constrained scheme for sparse coding on both steps. Specifically, we employ the m-nearest neighbors of a local feature in the image space to improve the consistency of coding. The benefit is that similar image features will be encoded with similar codewords, which reduced the stochasticity of a conventional coding strategy. We also show that the Viola–Jones algorithm, which is well-known in face detection, can be tailored to learning receptive fields, embedding the spatially constrained information on the pooling step. Extensive experiments on the UIUC sport event, 15 natural scenes and the Caltech 101 database suggests that scene categorization performance of several popular algorithms can be ubiquitously improved by incorporating the proposed two spatially constrained sparse coding scheme.     

Error-correcting pooling designs associated with some distance-regular graphs

Motivated by the pooling designs over the incidence matrices of matchings with various sizes of the complete graph K_2n considered by Ngo and Du [Ngo and Du, Discrete Math. 243 (2003) 167–170], two families of pooling designs over the incidence matrices oft-cliques (resp. strongly t-cliques) with various sizes of the Johnson graph J(n,t) (resp. the Grassmann graph J_q(n,t)) are considered. Their performances as pooling designs are better than those given by Ngo and Du. Moreover, pooling designs associated with other special distance-regular graphs are also considered.     

A bilinear approach to the pooling problem†

In this paper we present an algorithm for the pooling problem in refinery optimization based on a bilinear programming approach. The pooling problem occurs frequently in process optimization problems, especially refinery planning models. The main difficulty is that pooling causes an inherent nonlinearity in the otherwise linear models. We shall define the problem by formulating an aggregate mathematical model of a refinery, comment on solution methods for pooling problems that have been presented in the literature, and develop a new method based on convex approximations of the bilinear terms. The method is illustrated on numerical examples     

LRHW-AP: Using ranking-based metric as loss for Person Re-Identification

Optimizing a ranking-based metric as the loss function, such as Average Precision (AP), has been found very effective in image retrieval tasks, but it has received less attention in Person Re-Identification (Re-ID). In this paper, Low Rank High Weight (LRHW) AP is proposed to apply the AP-optimizing method on the Re-ID task. LRHW-AP employs high weight on the low rank positive instances, which provides more information for model optimization than high rank positive instances and distribute in high gradient area. We propose a new pooling method called Power Activation Weighted Mean (PAWM) pooling which can unify a set of pooling methods because of a changeable activation function and a trainable parameter. Thus one can adjust and train PAWM to adapt to the target task to improve the model performance. Besides, we incorporate Warmup and Exponentially Decay Scheduler with a delay period, called Warmup Delay Exponentially Decay Scheduler, which brings further improvement. Through an extensive set of ablation studies, we verify that all methods mentioned above contribute to the performance boosts on Re-ID and the model achieves 95.3% rank-1 and 88.4% mAP on Market1501 with ResNet50.     

Inventory models with lateral transshipments: A review

Lateral transshipments within an inventory system are stock movements between locations of the same echelon. These transshipments can be conducted periodically at predetermined points in time to proactively redistribute stock, or they can be used reactively as a method of meeting demand which cannot be satisfied from stock on hand. The elements of an inventory system considered, e.g. size, cost structures and service level definition, all influence the best method of transshipping. Models of many different systems have been considered. This paper provides a literature review which categorizes the research to date on lateral transshipments, so that these differences can be understood and gaps within the literature can be identified.     

Optimal consumption and portfolio choice for pooled annuity funds

This paper presents the optimal continuous time dynamic consumption and portfolio choice for pooled annuity funds. A pooled annuity fund constitutes an alternative way to protect against mortality risk compared to purchasing a life annuity. The crucial difference between the pooled annuity fund and purchase of a life annuity offered by an insurance company is that participants of a pooled annuity fund still have to bear some mortality risk while insured annuitants bear no mortality risk at all. The population of the pool is modelled by employing a Poisson process with time-dependent hazard-rate. It follows that the pool member’s optimization problem has to account for the stochastic investment horizon and for jumps in wealth which occur if another pool member dies. In case the number of pool members goes to infinity analytical solutions are provided. For finite pool sizes the solution of the optimization problem is reduced to the numerical solution of a set of ODEs. A simulation and welfare analysis show that pooled annuity funds insure very effectively against longevity risk even if their pool size is rather small. Only very risk averse investors or those without access to small pools are more inclined to pay a risk premium to access private life annuity markets in order to lay off mortality risk completely. As even families constitute such small pools the model provides theoretical justification for the low empirical annuity demand.     

SGSN＋MME融合组Pool策略研究

基于3GPP核心网融合演进背景和池组化技术分析,探讨了SGSN与MME融合组Pool的技术挑战以及相应解决方案,其中包括网络覆盖区域规划和网间标识映射方案,并对上述技术方案进行比较,最后针对现网部署给出网络融合组Pool策略的建议。