On a conjecture regarding Fisher information

Fisher's information measure plays a very important role in diverse areas of theoretical physics. The associated measures as functionals of quantum probability distributions defined in, respectively, coordinate and momentum spaces, are the protagonists of our present considerations. The product of them has been conjectured to exhibit a non trivial lower bound in [Phys. Rev. A (2000) 62 012107]. We show here that such is not the case. This is illustrated, in particular, for pure states that are solutions to the free-particle Schr\"odinger equation. In fact, we construct a family of counterexamples to the conjecture, corresponding to time-dependent solutions of the free-particle Schr\"odinger equation. We also give a new conjecture regarding any normalizable time-dependent solution of this equation.Comment: 4 pages; revised equations, results unchange

Comment on "Quantum discord through the generalized entropy in bipartite quantum states"

In [X.-W. Hou, Z.-P. Huang, S. Chen, Eur. Phys. J. D 68, 1 (2014)], Hou et al. present, using Tsallis' entropy, possible generalizations of the quantum discord measure, finding original results. As for the mutual informations and discord, we show here that these two types of quantifiers can take negative values. In the two qubits instance we further determine in which regions they are non-negative. Additionally, we study alternative generalizations on the basis of R\'enyi entropies.Comment: 5 pages, 4 figure

Using Networks To Understand Medical Data: The Case of Class III Malocclusions

A system of elements that interact or regulate each other can be represented by a mathematical object called a network. While network analysis has been successfully applied to high-throughput biological systems, less has been done regarding their application in more applied fields of medicine; here we show an application based on standard medical diagnostic data. We apply network analysis to Class III malocclusion, one of the most difficult to understand and treat orofacial anomaly. We hypothesize that different interactions of the skeletal components can contribute to pathological disequilibrium; in order to test this hypothesis, we apply network analysis to 532 Class III young female patients. The topology of the Class III malocclusion obtained by network analysis shows a strong co-occurrence of abnormal skeletal features. The pattern of these occurrences influences the vertical and horizontal balance of disharmony in skeletal form and position. Patients with more unbalanced orthodontic phenotypes show preponderance of the pathological skeletal nodes and minor relevance of adaptive dentoalveolar equilibrating nodes. Furthermore, by applying Power Graphs analysis we identify some functional modules among orthodontic nodes. These modules correspond to groups of tightly inter-related features and presumably constitute the key regulators of plasticity and the sites of unbalance of the growing dentofacial Class III system. The data of the present study show that, in their most basic abstraction level, the orofacial characteristics can be represented as graphs using nodes to represent orthodontic characteristics, and edges to represent their various types of interactions. The applications of this mathematical model could improve the interpretation of the quantitative, patient-specific information, and help to better targeting therapy. Last but not least, the methodology we have applied in analyzing orthodontic features can be applied easily to other fields of the medical science.</p

Injerto óseo en bloque usando como donante torus mandibular. Reporte de caso

Actualmente los materiales empleados para regeneración a través de injertos óseos están basados en compuestos sintéticos con propiedades en ocasiones poco predecibles para los pacientes. Los torus son exostosis óseas de etiología desconocida y pueden ser utilizados como injertos óseos con resultados clínicos exitosos. Así, el objetivo de este reporte de caso es describir la técnica quirúrgica de injerto óseo en bloque utilizando como donante torus mandibulares. Los resultados clínicos a 8 semanas postoperatorias evidenciaron tejidos en cicatrización y pocas molestias referidas por el paciente. Los injertos óseos provenientes de torus mandibulares son técnicas quirúrgicas de mediana complejidad que pueden ser empleados y permiten la obtención de resultados clínicos similares a los de otros materiales

Influence of Mathematics in The Desertion of Higher Education

In the present work the different models of university desertion are analyzed, identifying the factors that have influence in the continuation of the studies of the students. These factors are essentials to defining what will be understood by university desertion and to elaborate the profile of the deserter. In the case of the Universidad de Las Américas (Quito, Ecuador), the main factors that influence the desertion are corroborated with those that have been established according to the existing bibliography and a descriptive study of these data is carried out, in order to elaborate indicators that allow us to predict the behavior of the student population with a higher risk of dropping out. An analysis is made relating the area of Mathematics and the desertion, seeing how this area influences the possibility of a student dropping out. &nbsp