Well posedness of an integrodifferential kinetic model of Fokker-Planck type for angiogenesis.

Tumor induced angiogenesis processes including the effect of stochastic motion and branching of blood vessels can be described coupling a (nonlocal in time) integrodifferential kinetic equation of Fokker–Planck type with a diffusion equation for the tumor induced ingiogenic factor. The chemotactic force field depends on the flux of blood vessels through the angiogenic factor. We develop an existence and uniqueness theory for this system under natural assumptions on the initial data. The proof combines the construction of fundamental solutions for associated linearized problems with comparison principles, sharp estimates of the velocity integrals and compactness results for this type of kinetic and parabolic operators

Fundamental limitations in the purifications of tensor networks

We show a fundamental limitation in the description of quantum many-body mixed states with tensor networks in purification form. Namely, we show that there exist mixed states which can be represented as a translationally invariant (TI) matrix product density operator valid for all system sizes, but for which there does not exist a TI purification valid for all system sizes. The proof is based on an undecidable problem and on the uniqueness of canonical forms of matrix product states. The result also holds for classical states.

Análisis de la respuesta educativa desde la escuela a los menores en acogimiento residencial: un estudio de caso en la Comunidad de Madrid

The reality of children living in foster homes is clearly linked to the professionals that surround them both in the educational and residentialsphere. These are children who in all aspects of their livesat all hours, are exposed to the professionalism of those who work with them and not the affection of a family; their development is fully mediated by institutions. It is therefore a priority that teachers have specific training on children living infoster care, that general government (Education and Social Services) provide guidelines for action agreed to allow the coordination between the different professionals involved with children in foster care, considering the complexity of this coordination, as there are many institutions involved with these children: Social Services, schools, foster residences foster ... among others. Educational professionals have an important role in this intervention process, being their good professional work the one that favors a tight development of children in the educational field, but this intervention takes place generally from the ignorance of the specific situation faced by children living inresidential care and from the failure of the educational administration into sharing protocols, time and space, necessary for a proper coordination. In the event children incustody, and because of the uniqueness of their situation and the importance of a good intervention, there should be no space for improvisation.In addition intervention with children in residential care has to be based on a training and intervention from the complementary roles that is to be structured, systematic and evaluated in a continuously way by the professionals involved.We understand that the principle of equality in education requires to offer these minors an opportunity based on an appropriate intervention with formed professionals, knowledgeable and with the time and the necessary conditions...