Pyramids of n-Dimensional Generalized Maps

International audienceGraph pyramids are often used for representing irregular pyramids. Combinatorial pyramids have been recently defined for this purpose. We define here pyramids of n-dimensional generalized maps. This is the main contribution of this work: a generic definition in any dimension which extend and generalize the previous works. Moreover, such pyramids explicitly represent more topological information than graph pyramids. A pyramid can be implemented in several ways, and three representations are discussed in this paper

Dynamic pricing with demand learning under competition

Thesis (Ph. D.)--Massachusetts Institute of Technology, Sloan School of Management, Operations Research Center, 2007.This electronic version was submitted by the student author. The certified thesis is available in the Institute Archives and Special Collections.Includes bibliographical references (p. 199-204).In this thesis, we focus on oligopolistic markets for a single perishable product, where firms compete by setting prices (Bertrand competition) or by allocating quantities (Cournot competition) dynamically over a finite selling horizon. The price-demand relationship is modeled as a parametric function, whose parameters are unknown, but learned through a data driven approach. The market can be either in disequilibrium or in equilibrium. In disequilibrium, we consider simultaneously two forms of learning for the firm: (i) learning of its optimal pricing (resp. allocation) strategy, given its belief regarding its competitors' strategy; (ii) learning the parameters in the price-demand relationship. In equilibrium, each firm seeks to learn the parameters in the price-demand relationship for itself and its competitors, given that prices (resp. quantities) are in equilibrium. In this thesis, we first study the dynamic pricing (resp. allocation) problem when the parameters in the price-demand relationship are known. We then address the dynamic pricing (resp. allocation) problem with learning of the parameters in the price-demand relationship. We show that the problem can be formulated as a bilevel program in disequilibrium and as a Mathematical Program with Equilibrium Constraints (MPECs) in equilibrium. Using results from variational inequalities, bilevel programming and MPECs, we prove that learning the optimal strategies as well as the parameters, is achieved. Furthermore, we design a solution method for efficiently solving the problem. We prove convergence of this method analytically and discuss various insights through a computational study.(cont.) Finally, we consider closed-loop strategies in a duopoly market when demand is stochastic. Unlike open-loop policies (such policies are computed once and for all at the beginning of the time horizon), closed loop policies are computed at each time period, so that the firm can take advantage of having observed the past random disturbances in the market. In a closed-loop setting, subgame perfect equilibrium is the relevant notion of equilibrium. We investigate the existence and uniqueness of a subgame perfect equilibrium strategy, as well as approximations of the problem in order to be able to compute such policies more efficiently.by Carine Simon.Ph.D

The diagonal of the TT transform: computation and meaning

The TT-transform stands for time-time transform and has been derived as an inverse Fourier transform of the time-frequency S-transform. So far, it has been proposed that the diagonal of the TT-transform can be used for signal characterisation. We show here an alternative and simplified derivation of the TT-transform which enables a better understanding of this transform.Peer ReviewedPostprint (published version

The impact of the invasive alien plant, impatiens glandulifera, on pollen transfer networks

Biological invasions are a threat to the maintenance of ecological processes, including pollination. Plant-flower visitor networks are traditionally used as a surrogated for pollination at the community level, despite they do not represent the pollination process, which takes place at the stigma of plants where pollen grains are deposited. Here we investigated whether the invasion of the alien plant Impatiens glandulifera (Balsaminaceae) affects pollen transfer at the community level. We asked whether more alien pollen is deposited on the stigmas of plants on invaded sites, whether deposition is affected by stigma type (dry, semidry and wet) and whether the invasion of I. glandulifera changes the structure of the resulting pollen transfer networks. We sampled stigmas of plants on 10 sites invaded by I. glandulifera (hereafter, balsam) and 10 non-invaded control sites. All 20 networks had interactions with balsam pollen, although significantly more balsam pollen was found on plants with dry stigmas in invaded areas. Balsam pollen deposition was restricted to a small subset of plant species, which is surprising because pollinators are known to carry high loads of balsam pollen. Balsam invasion did not affect the loading of native pollen, nor did it affect pollen transfer network properties; networks were modular and poorly nested, both of which are likely to be related to the specificity of pollen transfer interactions. Our results indicate that pollination networks become more specialized when moving from the flower visitation to the level of pollen transfer networks. Therefore, caution is needed when inferring pollination from patterns of insect visitation or insect pollen loads as the relationship between these and pollen deposition is not straightforward. © 2015 Emer et al. This is an open access article distributed under the terms of the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited

The S-Transform From a Wavelet Point of View

Abstract—The -transform is becoming popular for time-frequency analysis and data-adaptive filtering thanks to its simplicity. While this transform works well in the continuous domain, its discrete version may fail to achieve accurate results. This paper compares and contrasts this transform with the better known continuous wavelet transform, and defines a relation between both. This connection allows a better understanding of the -transform, and makes it possible to employ the wavelet reconstruction formula as a new inverse -transform and to propose several methods to solve some of the main limitations of the discrete -transform, such as its restriction to linear frequency sampling.This work was supported by the projects SigSensual ref. CTM2004-04510-C03-02 and NEAREST CE-037110. The work of M. Schimmel was supported through the Ramon y Cajal and the Consolider-Ingenio 2010 Nr. CSD2006-00041 program.Peer reviewe