A classification of plane and planar 2-trees

We present new functional equations for the species of plane and of planar (in the sense of Harary and Palmer, 1973) 2-trees and some associated pointed species. We then deduce the explicit molecular expansion of these species, i.e a classification of their structures according to their stabilizers. There result explicit formulas in terms of Catalan numbers for their associated generating series, including the asymmetry index series. This work is closely related to the enumeration of polyene hydrocarbons of molecular formula C_nH_n+2.Comment: 26 pages, 14 figure

Sacrificing Accuracy for Reduced Computation: Cascaded Inference Based on Softmax Confidence

We study the tradeoff between computational effort and accuracy in a cascade of deep neural networks. During inference, early termination in the cascade is controlled by confidence levels derived directly from the softmax outputs of intermediate classifiers. The advantage of early termination is that classification is performed using less computation, thus adjusting the computational effort to the complexity of the input. Moreover, dynamic modification of confidence thresholds allow one to trade accuracy for computational effort without requiring retraining. Basing of early termination on softmax classifier outputs is justified by experimentation that demonstrates an almost linear relation between confidence levels in intermediate classifiers and accuracy. Our experimentation with architectures based on ResNet obtained the following results. (i) A speedup of 1.5 that sacrifices 1.4% accuracy with respect to the CIFAR-10 test set. (ii) A speedup of 1.19 that sacrifices 0.7% accuracy with respect to the CIFAR-100 test set. (iii) A speedup of 2.16 that sacrifices 1.4% accuracy with respect to the SVHN test set

Mise en place d’un laboratoire naturel sur le mont Covey Hill (Québec, Canada)

Le mont Covey Hill héberge des populations de salamandres rares et menacées dont les habitats sont maintenus en partie par\ud l’eau souterraine. Des travaux de recherche multidisciplinaires (UQAM, U. McGill, U. Montréal, IRBV, Centre Brace, SCABRIC et\ud ministères) ont permis de comprendre l’hydrologie ainsi que la répartition et les caractéristiques des habitats de salamandres. Ces projets ont contribué à la mise en place de stations de suivi écologique à long terme et de stations hydrométriques permanentes. En tant que propriétaire de terrains dédiés à la conservation, Conservation de la Nature assure la coordination de ces initiatives. Le mont Covey Hill est aujourd’hui un Laboratoire naturel unique au Québec, dédié à la compréhension intégrée et à long terme d’un écosystème fragile. Cet article a pour objectif de présenter le Laboratoire naturel par une description des recherches en cours et à venir

Intuitive human interactive with an arm robot for severely handicapped people - A one click approach.

International audienceAssistance to disabled people is still a domain in which a lot of progress needs to be done. The more severe the handicap is, more complex are the devices, implying increased efforts to simplify the interactions between man and these devices. In this document we propose a solution to reduce the interaction between a user and a robotic arm. The system is equipped with two cameras. One is fixed on the top of the wheelchair (eye-to-hand) and the other one is mounted on the end effector of the robotic arm (eye-in-hand). The two cameras cooperate to reduce the grasping task to one click. The method is generic, it does not require marks on the object, geometrical model or the database. It thus provides a tool applicable to any kind of graspable object. The paper first gives an overview of the existing grasping tools for disabled people and proposes a novel approach toward an intuitive human machine interaction

A high flux source of cold strontium atoms

We describe an experimental apparatus capable of achieving a high loading rate of strontium atoms in a magneto-optical trap operating in a high vacuum environment. A key innovation of this setup is a two dimensional magneto-optical trap deflector located after a Zeeman slower. We find a loading rate of 6x10^9/s whereas the lifetime of the magnetically trapped atoms in the 3P2 state is 54s.Comment: 12 pages, 16 figure

Area limit laws for symmetry classes of staircase polygons

We derive area limit laws for the various symmetry classes of staircase polygons on the square lattice, in a uniform ensemble where, for fixed perimeter, each polygon occurs with the same probability. This complements a previous study by Leroux and Rassart, where explicit expressions for the area and perimeter generating functions of these classes have been derived.Comment: 18 pages, 3 figure

Generalized shuffles related to Nijenhuis and TD-algebras

Shuffle and quasi-shuffle products are well-known in the mathematics literature. They are intimately related to Loday's dendriform algebras, and were extensively used to give explicit constructions of free commutative Rota-Baxter algebras. In the literature there exist at least two other Rota-Baxter type algebras, namely, the Nijenhuis algebra and the so-called TD-algebra. The explicit construction of the free unital commutative Nijenhuis algebra uses a modified quasi-shuffle product, called the right-shift shuffle. We show that another modification of the quasi-shuffle product, the so-called left-shift shuffle, can be used to give an explicit construction of the free unital commutative TD-algebra. We explore some basic properties of TD-operators and show that the free unital commutative Nijenhuis algebra is a TD-algebra. We relate our construction to Loday's unital commutative dendriform trialgebras, including the involutive case. The concept of Rota-Baxter, Nijenhuis and TD-bialgebras is introduced at the end and we show that any commutative bialgebra provides such objects.Comment: 20 pages, typos corrected, accepted for publication in Communications in Algebr