A study of the apsidal angle and a proof of monotonicity in the logarithmic potential case

This paper concerns the behaviour of the apsidal angle for orbits of central force system with homogenous potential of degree $-2\leq \alpha\leq 1$ and logarithmic potential. We derive a formula for the apsidal angle as a fixed-end points integral and we study the derivative of the apsidal angle with respect to the angular momentum $\ell$. The monotonicity of the apsidal angle as function of $\ell$ is discussed and it is proved in the logarithmic potential case.Comment: 24 pages, 1 figur

Rigorous numerics for NLS: bound states, spectra, and controllability

In this paper it is demonstrated how rigorous numerics may be applied to the one-dimensional nonlinear Schr\"odinger equation (NLS); specifically, to determining bound--state solutions and establishing certain spectral properties of the linearization. Since the results are rigorous, they can be used to complete a recent analytical proof [6] of the local exact controllability of NLS.Comment: 30 pages, 2 figure

Existence and instability of steady states for a triangular cross-diffusion system: a computer-assisted proof

In this paper, we present and apply a computer-assisted method to study steady states of a triangular cross-diffusion system. Our approach consist in an a posteriori validation procedure, that is based on using a fxed point argument around a numerically computed solution, in the spirit of the Newton-Kantorovich theorem. It allows us to prove the existence of various non homogeneous steady states for different parameter values. In some situations, we get as many as 13 coexisting steady states. We also apply the a posteriori validation procedure to study the linear stability of the obtained steady states, proving that many of them are in fact unstable

Learning the structure of Bayesian Networks: A quantitative assessment of the effect of different algorithmic schemes

One of the most challenging tasks when adopting Bayesian Networks (BNs) is the one of learning their structure from data. This task is complicated by the huge search space of possible solutions, and by the fact that the problem is NP-hard. Hence, full enumeration of all the possible solutions is not always feasible and approximations are often required. However, to the best of our knowledge, a quantitative analysis of the performance and characteristics of the different heuristics to solve this problem has never been done before. For this reason, in this work, we provide a detailed comparison of many different state-of-the-arts methods for structural learning on simulated data considering both BNs with discrete and continuous variables, and with different rates of noise in the data. In particular, we investigate the performance of different widespread scores and algorithmic approaches proposed for the inference and the statistical pitfalls within them

A method to rigorously enclose eigenpairs of complex interval matrices

summary:In this paper, a rigorous computational method to enclose eigenpairs of complex interval matrices is proposed. Each eigenpair x=(\lambda,\rv) is found by solving a nonlinear equation of the form $f(x)=0$ via a contraction argument. The set-up of the method relies on the notion of {\em radii polynomials}, which provide an efficient mean of determining a domain on which the contraction mapping theorem is applicable

A stacking-based artificial intelligence framework for an effective detection and localization of colon polyps

Albuquerque, C., Henriques, R., & Castelli, M. (2022). A stacking-based artificial intelligence framework for an effective detection and localization of colon polyps. Scientific Reports, 12, 1-12. [17678]. https://doi.org/10.21203/rs.3.rs-1862362/v1, https://doi.org/10.1038/s41598-022-21574-w ------- This work was supported by national funds through FCT (Fundação para a Ciência e a Tecnologia), under the project - UIDB/04152/2020 - Centro de Investigação em Gestão de Informação (MagIC)/NOVA IMS.Polyp detection through colonoscopy is a widely used method to prevent colorectal cancer. The automation of this process aided by artificial intelligence allows faster and improved detection of polyps that can be missed during a standard colonoscopy. In this work, we propose implementing different object detection algorithms for polyp detection. To improve the mean average precision (mAP) of the detection, we combine the baseline models through a stacking approach. The experiments demonstrate the potential of this new methodology, which can reduce the workload for oncologists and increase the precision of the localization of polyps. Our proposal achieves an mAP of 0.86, translated into an improvement of 34.9% compared to the best baseline model and 28.8% with respect to the weighted boxes fusion ensemble technique.preprintpublishersversionepub_ahead_of_prin

Analytic enclosure of the fundamental matrix solution

This work describes a method to rigorously compute the real Floquet normal form decomposition of the fundamental matrix solution of a system of linear ODEs having periodic coefficients. The Floquet normal form is validated in the space of analytic functions. The technique combines analytical estimates and rigorous numerical computations and no rigorous integration is needed. An application to the theory of dynamical system is presented, together with a comparison with the results obtained by computing the enclosure in the C s category