arXiv subjects

M. M. Ruiz

Publications and source records attributed to M. M. Ruiz.

5 recordsLinked to original sources

arXiv2025

Optimal control of counter-terrorism tactics

This paper presents an optimal control problem to analyze the efficacy of counter-terrorism tactics. We present an algorithm that efficiently combines the Minimum Principle of Pontryagin, the shooting method and the cyclic descent of coordinates. We also present a result that allows us to know a priori the steady state solutions. Using this technique we are able to choose parameters that reach a specific solution, of which there are two. Numerical examples are presented to illustrate the possibilities of the method. Finally, we study the sufficient conditions for optimality and suggest an improvement on the functional which also guarantees local optimality.

math.OC↗

arXiv2022

A new method for computing asymptotic results in optimal stopping problems

In this paper, we present a novel method for computing the asymptotic values of both the optimal threshold, and the probability of success in sequences of optimal stopping problems. This method, based on the resolution of a first-order linear differential equation, makes it possible to systematically obtain these values in many situations. As an example, we address nine variants of the well-known secretary problem, including the classical one, that appear in the literature on the subject, as well as four other unpublished ones.

math.PR↗

arXiv2020

The multi-returning secretary problem

In this paper we consider the so-called Multi-returning secretary problem, a version of the Secretary problem in which each candidate has $m$ identical copies. The case $m=2$ has already been completely solved by several authors using different methods both the case $m>2$ had not been satisfactorily solved yet. Here, we provide and efficient algorithm to compute the optimal threshold and the probability of success for every $m$. Moreover, we give a method to determine their asymtoptic values based on the solution of a system of $m$ ODEs.

math.PR↗

arXiv2020

MNIST-NET10: A heterogeneous deep networks fusion based on the degree of certainty to reach 0.1 error rate. Ensembles overview and proposal

Ensemble methods have been widely used for improving the results of the best single classificationmodel. A large body of works have achieved better performance mainly by applying one specific ensemble method. However, very few works have explored complex fusion schemes using het-erogeneous ensembles with new aggregation strategies. This paper is three-fold: 1) It provides an overview of the most popular ensemble methods, 2) analyzes several fusion schemes using MNIST as guiding thread and 3) introduces MNIST-NET10, a complex heterogeneous fusion architecture based on a degree of certainty aggregation approach; it combines two heterogeneous schemes from the perspective of data, model and fusion strategy. MNIST-NET10 reaches a new record in MNISTwith only 10 misclassified images. Our analysis shows that such complex heterogeneous fusionarchitectures based on the degree of certainty can be considered as a way of taking benefit fromdiversity.

cs.LG↗

arXiv2017

The Best-or-Worst and the Postdoc problems

We consider two variants of the secretary problem, the\emph{ Best-or-Worst} and the \emph{Postdoc} problems, which are closely related. First, we prove that both variants, in their standard form with binary payoff 1 or 0, share the same optimal stopping rule. We also consider additional cost/perquisites depending on the number of interviewed candidates. In these situations the optimal strategies are very different. Finally, we also focus on the Best-or-Worst variant with different payments depending on whether the selected candidate is the best or the worst.

math.PR↗