Compositional evolution with mass transfer in closed systems

Evolution of compositions in time, space, temperature or other covariates is frequent in practice. For instance, the radioactive decomposition of a sample changes its composition with time. Some of the involved isotopes decompose into other isotopes of the sample, thus producing a transfer of mass from some components to other ones, but preserving the total mass present in the system. This evolution is traditionally modelled as a system of ordinary di erential equations of the mass of each component. However, this kind of evolution can be decomposed into a compositional change, expressed in terms of simplicial derivatives, and a mass evolution (constant in this example). A rst result is that the simplicial system of di erential equations is non-linear, despite of some subcompositions behaving linearly. The goal is to study the characteristics of such simplicial systems of di erential equa- tions such as linearity and stability. This is performed extracting the compositional dif ferential equations from the mass equations. Then, simplicial derivatives are expressed in coordinates of the simplex, thus reducing the problem to the standard theory of systems of di erential equations, including stability. The characterisation of stability of these non-linear systems relays on the linearisation of the system of di erential equations at the stationary point, if any. The eigenvelues of the linearised matrix and the associated behaviour of the orbits are the main tools. For a three component system, these orbits can be plotted both in coordinates of the simplex or in a ternary diagram. A characterisation of processes with transfer of mass in closed systems in terms of stability is thus concluded. Two examples are presented for illustration, one of them is a radioactive decay

Survival of European patients diagnosed with lymphoid neoplasms in 2000-2002: results of the HAEMACARE project

The European Cancer Registry-based project on hematologic malignancies (HAEMACARE), set up to improve the availability and standardization of data on hematologic malignancies in Europe, used the European Cancer Registry-based project on survival and care of cancer patients (EUROCARE-4) database to produce a new grouping of hematologic neoplasma(defined by the International Classification of Diseases for Oncology, Third Edition and the 2001/2008 World Health Organization classifications) for epidemiological and public health purposes. We analyzed survival for lymphoid neoplasms in Europe by disease group, comparing survival between different European regions by age and sex. Design and Methods Incident neoplasms recorded between 1995 to 2002 in 48 population-based cancer registries in 20 countries participating in EUROCARE-4 were analyzed. The period approach was used to estimate 5-year relative survival rates for patients diagnosed in 2000-2002, who did not have 5 years of follow up. Results: The 5-year relative survival rate was 57% overall but varied markedly between the defined groups. Variation in survival within the groups was relatively limited across European regions and less than in previous years. Survival differences between men and women were small. The relative survival for patients with all lymphoid neoplasms decreased substantially after the age of 50. The proportion of ‘not otherwise specified’ diagnoses increased with advancing age.Conclusions: This is the first study to analyze survival of patients with lymphoid neoplasms, divided into groups characterized by similar epidemiological and clinical characteristics, providing a benchmark for more detailed analyses. This Europe-wide study suggests that previously noted differences in survival between regions have tended to decrease. The survival of patients with all neoplasms decreased markedly with age, while the proportion of ‘not otherwise specified’ diagnoses increased with advancing age. Thus the quality of diagnostic work-up and care decreased with age, suggesting that older patients may not be receiving optimal treatment

Psychological and Family Factors Associated with Suicidal Ideation in Pre-Adolescents

To assess the psychological and family factors associated with suicidal ideation in preadolescent children, we studied a sample of 361 students, average age 9 years old. Two groups were formed, on the basis of the presence (n = 34) or absence (n = 44) of suicidal ideation. Suicidal ideation was assessed with the Children’s Depression Inventory and the Children’s Depression Rating Scale-Revised. Depression, hopelessness, self-esteem, and perceived family environment were compared in both the suicidal ideation and the control groups. Students with suicidal ideation generally presented greater depressive symptoms and hopelessness, and lower self-esteem and family expressiveness, although there were differences both between sexes, and when the variable depression was controlled. Identifying these risk factors in pre-adolescents may have an impact on prevention of suicidal behavior at higher risk ages