Methods of Prediction of Infantile Hemangioma Evolution

Cutaneous hemangioma is the most frequent benign tumor for children. This blood anomaly has a frequency of 10% for children and is more common for females than males. Infantile hemangioma appears soon after birth and, in general, after a period of evolution it regresses by itself. The hemangiomas appear with a high frequency on face and neck and, if they don’t regress completely, they may have psychological effects. Sometimes, depending on the size and location of the hemangioma (mainly on the face), a quick decision should be taken to proceed (or not) with surgery, so that the lesions do not cause permanent disfigurement of the patient. Yet, doctors do not know at the moment if, at a given moment of time, how much a hemangioma will progress in the near future. Therefore, an automatic monitoring system for the detection and evaluation of the evolution of hemangiomas would be a useful tool for physicians, helping them in their decision about treatment. The present lecture presents ongoing work on developing such a system. Based on a series of images of the same hemangioma acquired periodically (typically, one month passes between two successive medical controls for a single patient), we aim at firstly assessing the way the hemangioma evolves over time, and, secondly, at predicting its evolution in the near future. This involves segmenting the hemangioma area, which is made difficult by the variety of shapes and colors the tumor may take. Then, two parameters are computed for each hemangioma, namely, size and degree of redness, as being the factors of most significant importance for assessing the state of the tumor at a given time. A fuzzy system (which incorporates knowledge from experienced physicians) is then developed based on the two aforementioned parameters to assess the evolution of the tumor in time.Universidad de Málaga. Campus de Excelencia Internacional Andalucía Tech

Positive or negative Poynting effect? The role of adscititious inequalities in hyperelastic materials

Motivated by recent experiments on biopolymer gels whereby the reverse of the usual (positive) Poynting effect was observed, we investigate the effect of the so-called “adscititious inequalities” on the behaviour of hyperelastic materials subject to shear. We first demonstrate that for homogeneous isotropic materials subject to pure shear, the resulting deformation consists of a triaxial stretch combined with a simple shear in the direction of the shear force if and only if the Baker-Ericksen inequalities hold. Then for a cube deformed under pure shear, the positive Poynting effect occurs if the “sheared faces spread apart”, whereas the negative Poynting effect is obtained if the “sheared faces draw together”. Similarly, under simple shear deformation, the positive Poynting effect is obtained if the “sheared faces tend to spread apart”, whereas the negative Poynting effect occurs if the “sheared faces tend to draw together”. When the Poynting effect occurs under simple shear, it is reasonable to assume that the same sign Poynting effect is obtained also under pure shear. Since the observation of the negative Poynting effect in semiflexible biopolymers implies that the (stronger) empirical inequalities may not hold, we conclude that these inequalities must not be imposed when such materials are described

Real Second Order Freeness and Haar Orthogonal Matrices

We demonstrate the asymptotic real second order freeness of Haar distributed orthogonal matrices and an independent ensemble of random matrices. Our main result states that if we have two independent ensembles of random matrices with a real second order limit distribution and one of them is invariant under conjugation by an orthogonal matrix, then the two ensembles are asymptotically real second order free. This captures the known examples of asymptotic real second order freeness introduced by Redelmeier [R1, R2].Comment: 50 pages, revision has refreshed references and corrected typo

Amplifying ultraweak transitions in collective systems via quantum interference

We investigate laser-induced quantum interference phenomena in superradiance processes and in an ensemble of initially excited $\Lambda-$type closely packed three-level emitters. The lower doublet levels are pumped with a coherent laser field. Due to constructive quantum interference effects, the superradiance occurs on a much weaker atomic transition which is not the case in the absence of the coherent driving. This result may be of visible relevance for enhancing ultraweak transitions in atomic or atomic-like systems, respectively, or for high-frequency lasing effects.Comment: 12 pages, 3 figure