Krull-tropical hypersurfaces

The concepts of tropical-semiring and tropical hypersurface, are extended for an arbitrary ordered group. Then, we define the tropicalization of a polynomial with coefficients in a Krull-valued field. After a close study of the properties of the operator "tropicalization" we conclude with an extension of Kapranov's theorem to algebraically closed fields together with a valuation over an ordered group.Comment: 12 page

Support of Laurent series algebraic over the field of formal power series

This work is devoted to the study of the support of a Laurent series in several variables which is algebraic over the ring of power series over a characteristic zero field. Our first result is the existence of a kind of maximal dual cone of the support of such a Laurent series. As an application of this result we provide a gap theorem for Laurent series which are algebraic over the field of formal power series. We also relate these results to diophantine properties of the fields of Laurent series.Comment: 31 pages. To appear in Proc. London Math. So

Newton's lemma for differential equations

The Newton method for plane algebraic curves is based on the following remark: the first term of a series, root of a polynomial with coefficients in the ring of series in one variable, is a solution of an initial equation that can be determined by the Newton polygon. Given a monomial ordering in the ring of polynomials in several variables, we describe the systems of initial equations that satisfy the first terms of the solutions of a system of partial differential equations. As a consequence, we extend Mora and Robbiano’s Groebner fan to differential ideals

What seems to explain suicidality in Yucatan Mexican young adults? findings from an app-based mental health screening test using the SMART-SCREEN protocol

The relationship between suicidality, depression, anxiety, and well-being was explored in young adults (median age 20.7 years) from the State of Yucatan (Mexico), which has a suicide rate double that of other Mexican states. A cross-sectional study was carried out in 20 universities in Yucatan and 9,366 students were surveyed using validated questionnaires built into a smartphone app, applying partial least squares structural equation models. High suicide risk was assessed in 10.8% of the sample. Clinically relevant depression and anxiety levels were found in 6.6% and 10.5% of the sample, respectively, and 67.8% reported high well-being. Comparably higher levels of suicide risk, depression and anxiety, and lower well-being were found in women, who were also somewhat older than men in our study. Furthermore, path analysis in the structural equation model revealed that depression was the main predictor of suicidal behaviour as well as of higher anxiety levels and lower self-perceived well-being in the total sample and in both genders. Our findings draw attention to the association between suicidality, depression, anxiety, and well-being in Yucatan young adults and gender differences with this regard. Mental health screening via smartphone might be a useful tool to reach large populations and contribute to mental health policies, including regional suicide prevention effortsOpen Access funding provided thanks to the CRUE-CSIC agreement with Springer Nature. No funding was received for this stud

WHODAS 2.0 as a Measure of Severity of Illness: Results of a FLDA Analysis

WHODAS 2.0 is the standard measure of disability promoted by World Health Organization whereas Clinical Global Impression (CGI) is a widely used scale for determining severity of mental illness. Although a close relationship between these two scales would be expected, there are no relevant studies on the topic. In this study, we explore if WHODAS 2.0 can be used for identifying severity of illness measured by CGI using the Fisher Linear Discriminant Analysis (FLDA) and for identifying which individual items of WHODAS 2.0 best predict CGI scores given by clinicians. One hundred and twenty-two patients were assessed with WHODAS 2.0 and CGI during three months in outpatient mental health facilities of four hospitals of Madrid, Spain. Compared with the traditional correction of WHODAS 2.0, FLDA improves accuracy in near 15%, and so, with FLDA WHODAS 2.0 classifying correctly 59.0% of the patients. Furthermore, FLDA identifies item 6.6 (illness effect on personal finances) and item 4.5 (damaged sexual life) as the most important items for clinicians to score the severity of illness

Universal mental health screening with a focus on suicidal behaviour using smartphones in a Mexican rural community: Protocol for the SMART-SCREEN population-based survey

Introduction Mental disorders represent the second cause of years lived with disability worldwide. Suicide mortality has been targeted as a key public health concern by the WHO. Smartphone technology provides a huge potential to develop massive and fast surveys. Given the vast cultural diversity of Mexico and its abrupt orography, smartphone-based resources are invaluable in order to adequately manage resources, services and preventive measures in the population. The objective of this study is to conduct a universal suicide risk screening in a rural area of Mexico, measuring also other mental health outcomes such as depression, anxiety and alcohol and substance use disorders. Methods and analysis A population-based cross-sectional study with a temporary sampling space of 9 months will be performed between September 2019 and June 2020. We expect to recruit a large percentage of the target population (at least 70%) in a short-term survey of Milpa Alta Delegation, which accounts for 137 927 inhabitants in a territorial extension of 288 km 2. They will be recruited via an institutional call and a massive public campaign to fill in an online questionnaire through mobile-assisted or computer-assisted web app. This questionnaire will include data on general health, validated questionnaires including Well-being Index 5, Patient Health Questionnaire-9, Generalized Anxiety Disorder Scale 2, Alcohol Use Disorders Identification Test, selected questions of the Drug Abuse Screening Test and Columbia-Suicide Severity Rating Scales and Diagnostic and statistical manual of mental disorders (DSM-5) questions about self-harm. We will take into account information regarding time to mobile app response and geo-spatial location, and aggregated data on social, demographical and environmental variables. Traditional regression modelling, multilevel mixed methods and data-driven machine learning approaches will be used to test hypotheses regarding suicide risk factors at the individual and the population level. Ethics and dissemination Ethical approval (002/2019) was granted by the Ethics Review Board of the Hospital Psiquiátrico Yucatán, Yucatán (Mexico). This protocol has been registered in ClinicalTrials.gov. The starting date of the study is 3 September 2019. Results will serve for the planning and healthcare of groups with greater mental health needs and will be disseminated via publications in peer-reviewed journal and presented at relevant mental health conferences. Trial registration number NCT04067063