Non-existence of an invariant measure for a homogeneous ellipsoid rolling on the plane

It is known that the reduced equations for an axially symmetric homogeneous ellipsoid that rolls without slipping on the plane possess a smooth invariant measure. We show that such an invariant measure does not exist in the case when all of the semi-axes of the ellipsoid have different length.Comment: v2: Minor changes after journal review. This text uses the theory developed in arXiv:1304.1788 for the specific example of a homogeneous ellipsoid rolling on the plan

Teaching-innovation experience in competitiveness and innovation in business

The aim of this paper is to contrast the students’ opinions about the teaching innovation experience carried out in the subject “Competitividad en Innovación en la Empresa” (Competitiveness and Innovation in Business). The procedure will start with the subject’s profile, going through the main objectives and teaching methodology, to finish with evaluation and assessment, as suggested in the subject’s syllabus for the academic year 2007/08. Taking this as a starting point and, due to the fact that the number of students in the control group is not very high, we suggest changing both the teaching methodology and the evaluation. These changes will be contrasted with the students’ acceptance and involvement.PROCEEDINGS C

Topological entropy and periods of self–maps on compact manifolds

Let (M; f) be a discrete dynamical system induced by a self{map f defined on a smooth compact connected n{dimensional manifold M. We provide sufficient conditions in terms of the Lefschetz zeta function in order that: (1) f has positive topological entropy when f is C1, and (2) f has infinitely many periodic points when f is C1 and f(M) ⊆ Int(M). Moreover, for the particular manifolds Sn, Sn x Sm, CPn and HPn we improve the previous sufficient conditions.The first author of this work was partially supported by MINECO grant number MTM2014-51891-P and Fundación Séneca de la Región de Murcia grant number 19219/PI/14. The second author is partially supported by a MINECO grant MTM2013-40998-P, an AGAUR grant number 2014SGR-568, and the grants FP7-PEOPLE-2012-IRSES 318999 and 316338

Distance-based kernels for real-valued data

We consider distance-based similarity measures for real-valued vectors of interest in kernel-based machine learning algorithms. In particular, a truncated Euclidean similarity measure and a self-normalized similarity measure related to the Canberra distance. It is proved that they are positive semi-definite (p.s.d.), thus facilitating their use in kernel-based methods, like the Support Vector Machine, a very popular machine learning tool. These kernels may be better suited than standard kernels (like the RBF) in certain situations, that are described in the paper. Some rather general results concerning positivity properties are presented in detail as well as some interesting ways of proving the p.s.d. property.Peer ReviewedPostprint (author's final draft

Deep neural network for traffic sign recognition systems: An analysis of spatial transformers and stochastic optimisation methods

This paper presents a Deep Learning approach for traffic sign recognition systems. Several classification experiments are conducted over publicly available traffic sign datasets from Germany and Belgium using a Deep Neural Network which comprises Convolutional layers and Spatial Transformer Networks. Such trials are built to measure the impact of diverse factors with the end goal of designing a Convolutional Neural Network that can improve the state-of-the-art of traffic sign classification task. First, different adaptive and non-adaptive stochastic gradient descent optimisation algorithms such as SGD, SGD-Nesterov, RMSprop and Adam are evaluated. Subsequently, multiple combinations of Spatial Transformer Networks placed at distinct positions within the main neural network are analysed. The recognition rate of the proposed Convolutional Neural Network reports an accuracy of 99.71% in the German Traffic Sign Recognition Benchmark, outperforming previous state-of-the-art methods and also being more efficient in terms of memory requirements.Ministerio de Economía y Competitividad TIN2017-82113-C2-1-RMinisterio de Economía y Competitividad TIN2013-46801-C4-1-

Evaluation of subsidies programs to sell green cars: Impact on prices, quantities and efficiency

During the recent period of economic crisis, many countries have introduced scrappage schemes to boost the sale and production of vehicles, particularly of vehicles designed to pollute less. In this paper, we analyze the impact of a particular scheme in Spain (Plan2000E) on vehicle prices and sales figures as well as on the reduction of polluting emissions from vehicles on the road. We considered the introduction of this scheme an exogenous policy change and because we could distinguish a control group (non-subsidized vehicles) and a treatment group (subsidized vehicles), before and after the introduction of the Plan, we were able to carry out our analysis as a quasi-natural experiment. Our study reveals that manufacturers increased vehicle prices by the same amount they were granted through the Plan (1,000 €). In terms of sales, econometric estimations revealed an increase of almost 5% as a result of the implementation of the Plan. With regard to environmental efficiency, we compared the costs (inverted quantity of money) and the benefits of the program (reductions in polluting emissions and additional fiscal revenues) and found that the Plan would only be beneficial if it boosted demand by at least 30%.Subsidies; Automobile sector; Difference-in-Difference estimator; Green policies.

Topological entropy of continuous self–maps on a graph

Let G be a graph and f be a continuous self–map on G. We provide sufficient conditions based on the Lefschetz zeta function in order that f has positive topological entropy. Moreover, for the particular graphs: p–flower graph, n-lips graph and (p+r1L1+:::+rsLs)–graph we are able to go further and state more precise conditions for having positive topological entropy.The second author is partially supported by the Ministerio de Economía, Industria y Competitividad, Agencia Estatal de Investigación grants MTM-2016-77278-P (FEDER) and MDM-2014-0445, the Agència de Gestió d’Ajuts Universitaris i de Recerca grant 2017SGR1617, and the H2020 European Research Council grant MSCA-RISE-2017-777911