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We study the algebraic closure of $\mathbb K(\!(x)\!)$, the field of power series in several indeterminates over a field $\mathbb K$. In characteristic zero we show that the elements algebraic over $\mathbb K(\!(x)\!)$ can be expressed as Puiseux series such that the convex hull of its support is essentially a polyhedral rational cone, strengthening the known results. In positive characteristic we construct algebraic closed fields containing the field of power series and we give examples showing that the results proved in characteristic zero are longer valid in positive characteristic., The positive characteristic case has been completely changed after Diane Maclagan pointed out a mistake in the previous version. Final version. To appear in Math. Annalen

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 efforts, Open Access funding provided thanks to the CRUE-CSIC agreement with Springer Nature. No funding was received for this study

Let $f$ be a polynomial function over the complex numbers and let $\phi$ be a smooth function over $\mathbb{C}$ with compact support. When $f$ is non-degenerate with respect to its Newton polyhedron, we give an explicit list of candidate poles for the complex local zeta function attached to $f$ and $\phi$. The provided list is given just in terms of the normal vectors to the supporting hyperplanes of the Newton polyhedron attached to $f$. More precisely, our list does not contain the candidate poles coming from the additional vectors required in the regular conical subdivision of the first orthant, and necessary in the study of local zeta functions through resolution of singularities. Our results refine the corresponding results of Varchenko and generalize the results of Denef and Sargos in the real case, to the complex setting., Comment: 19 pages. Comments welcome!

IntroductionMental 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 analysisA 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 km2.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 disseminationEthical 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 numberNCT04067063.

International audience; BACKGROUND:Anhedonia is defined as the lack of enjoyment, engagement in, or energy for life's experiences. Only two scales to measure anhedonia have been adapted for use in Spanish-speaking populations. The aim of this study was to determine the reliability and validity of the Dimensional Anhedonia Rating Scale (DARS) following translation and adaptation for Spanish population.METHOD:The study sample included 134 patients over 18 years of age with a range of psychiatric diagnoses. Those with substance use, decompensated medical conditions, illiteracy, or lack of fluency in Spanish were excluded. The structure of the Spanish adaptation was evaluated through factor analysis. Internal reliability was assessed through Cronbach's alpha and validity was measured using Pearson's correlation between total scores for DARS and its subscales and SHAPS score.RESULTS:A strong internal consistency was observed (Cronbach alpha = 0.92 for total scale score and 0.91-0.92 for subscale scores). Similarly, a significant and strong correlation between total scores for DARS and SHAPS was found (r = 0.51, p

In this article we focus on the study of special parabolic points in surfaces arising as graphs of polynomials, we prove that Viro’s construction glues a class of special parabolic points that we call transversal and build families of real polynomials in two variables with a prescribed number of special parabolic points in their graphs. When $$13\le d\le $$ 10,000, we use this result to build a family of degree d real polynomials in two variables with $$(d-4)(2d-9)$$ special parabolic points in its graph. This brings the number of special parabolic points closer to the upper bound of $$(d-2)(5d-12)$$ which is the best known up until now.

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.

Background and objectives Technology based assessments are being used for screening and monitoring in a wide scope of medical specialties, including mental health field. Depression and anxiety are common disorders in which e-health tools can be useful. We aimed to compare clinician assessment of illness severity in patients with depression and anxiety diagnosis with computer-based self-assessment within 24 h of clinician evaluation via MEmind ( www.memind.net ), a novel web-tool. Methods From May 2014, adult patients attended in outpatient settings in Fundacion Jimenez Diaz Psychiatry Department were registered in MEmind, a web tool designed for psychiatric assessment. During the recruitment, clinicians use CGI-S for patient assessment via MEmind and provide patients a code and password to use the web-tool. We selected those patients diagnosed with depression and/or anxiety who connected within 24 h of the clinical visit and complete in the web page GHQ and WHO-5 scales. We calculated a bivariate correlation for CGI-S, WHO-5 and GHQ-12. Results Of the 231 participants, 157 (68%) were diagnosed with anxiety disorders and 74 (32%) with depression. Using the Spearman Rho test for correlation, we found a low correlation between CGI-S and total WHO-5 (r = −0.192; p = 0.006) and between CGI-S and total GHQ-12 (r = 0.211; p = 0.002) and a good correlation between total WHO-5 and total GQH-12 (r = −0.606; p = 0.000). Conclusions We found a low correlation between clinician assessment and patients’ self-reports within 24 h of clinician evaluation. Factors that potentially influenced the degree of correlation related with patients, clinicians, measurements and technology are discussed.

Resumen Introduccion El auge de la telemedicina en el campo de la salud mental esta haciendo que el uso de instrumentos psicometricos, tradicionalmente basados en un soporte de «lapiz-y-papel», se adapte al formato electronico. El objetivo de este trabajo es verificar si los 2 formatos de conocidos instrumentos como las escalas GHQ-12, WHO-5 y PHQ-9 son intercambiables. Material y metodos Cuarenta y siete voluntarios completaron los cuestionarios GHQ-12, WHO-5 y PHQ-9 en papel y en las siguientes 24 h en su version electronica a traves de la web www.memind.net (24 en formato electronico-Likert y 23 en formato electronico-slider). Se midio la consistencia interna mediante el indice α-Cronbach y el coeficiente omega, la fiabilidad test-retest mediante el coeficiente de correlacion intraclase (CCI), el grado de acuerdo de los items mediante el coeficiente kappa ponderado y comparamos la estructura dimensional de los 2 formatos con el indice de ajuste comparativo (IAC). Resultados La consistencia interna de los instrumentos fue mayor de 0,8 para todos los instrumentos a excepcion del PHQ-9. Los CCI oscilaron entre 0,655 para PHQ-9 lapiz-y-papel/electronico-slider y 0,901 para GHQ-12 lapiz-y-papel/electronico-slider. El acuerdo entre los items en las versiones en lapiz-y-papel y electronica-Likert fue variable, desde acuerdos muy bajos en el del item PHQ-1 (κ ponderada = 0,143; p = 0,384) hasta acuerdos altos en el item PHQ-5 (κ ponderada = 0,769; p = 0,000). La equivalencia arrojada con el IAC fue adecuada. Conclusiones Con la excepcion del PHQ-9 electronico-Likert, los cuestionarios mantienen su estructura en la version electronica. Encontramos discrepancias en el acuerdo entre los items, lo que apoya la idea de que el paso de un instrumento disenado en papel al medio digital no es un proceso automatico, sino que requiere un proceso de adaptacion y de verificacion sobre el tipo de diseno en formato electronico.

We construct an explicit filtration of the ring of algebraic power series by finite dimensional constructible sets, measuring the complexity of these series. As an application, we give a bound on the dimension of the set of algebraic power series of bounded complexity lying on an algebraic variety defined over the field of power series., 12 pages

Resumen Introduccion El acuerdo entre-examinadores es un aspecto fundamental en la planificacion de cualquier trabajo de investigacion donde la principal herramienta diagnostica es la entrevista clinica. El objetivo de este estudio es valorar el acuerdo entre-examinadores de un instrumento de evaluacion de la conducta suicida (Protocolo breve de evaluacion del suicidio) utilizando las valoraciones de multiples observadores en una sola sesion. Metodo Durante la fase piloto de un estudio clinico multicentrico centrado en la monitorizacion de intentos de suicidio, 32 examinadores evaluaron el video de la entrevista clinica a un paciente simulado con conducta suicida. Para identificar los items en los que existia una mayor discordancia y a los examinadores cuyo criterio se alejaba mas del acuerdo general, se utilizo el metodo Detection Of Multiple Examiners Not In Consensus (DOMENIC). Resultado El acuerdo interexaminadores oscilo entre pobre ( Conclusiones El diseno propuesto permite evaluar el acuerdo entre-examinadores de una forma eficiente (en una unica sesion). Ademas, con respecto al Protocolo breve de evaluacion del suicidio, el acuerdo entre-examinadores fue apropiado.

Introduction: Inter-rater agreement is a crucial aspect in the planning and performance of a clinical trial in which the main assessment tool is the clinical interview. The main objectives of this study are to study the inter-rater agreement of a tool for the assessment of suicidal behavior (Brief Suicide Questionnaire) and to examine whether the inter-examiner agreement when multiple ratings are made on a single subject is an efficient method to assess the reliability of an instrument. Method: In the context of designing a multicenter clinical trial, 32 psychiatrists assessed a videotaped clinical interview of a patient with suicidal behavior. In order to identify those items in which a greater level of discordance existed and detect the examiners whose ratings differed significantly from the average ratings, we used the DOMENIC method (Detecion of Multiple Examiners Not in Consensus). Results: Inter-rater agreement was between poor (

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., 12 pages

Let $I$ be an ideal of the ring of Laurent polynomials $K[x_1^{\pm1},\ldots,x_n^{\pm1}]$ with coefficients in a real-valued field $(K,v)$. The fundamental theorem of tropical algebraic geometry states the equality $\text{trop}(V(I))=V(\text{trop}(I))$ between the tropicalization $\text{trop}(V(I))$ of the closed subscheme $V(I)\subset (K^*)^n$ and the tropical variety $V(\text{trop}(I))$ associated to the tropicalization of the ideal $\text{trop}(I)$. In this work we prove an analogous result for a differential ideal $G$ of the ring of differential polynomials $K[[t]]\{x_1,\ldots,x_n\}$, where $K$ is an uncountable algebraically closed field of characteristic zero. We define the tropicalization $\text{trop}(\text{Sol}(G))$ of the set of solutions $\text{Sol}(G)\subset K[[t]]^n$ of $G$, and the set of solutions associated to the tropicalization of the ideal $\text{trop}(G)$. These two sets are linked by a tropicalization morphism $\text{trop}:\text{Sol}(G)\longrightarrow \text{Sol}(\text{trop}(G))$. We show the equality $\text{trop}(\text{Sol}(G))=\text{Sol}(\text{trop}(G))$, answering a question raised by D. Grigoriev earlier this year., 11 pages, abstract added, simplification of proofs in Sections 6 and 7, added references for Sections 1 and 7. To appear in the Pacific Journal of Mathematics

The Newton polygon construction for ODEs, and Malgrange–Ramis polygon for partial differential equations in one variable are generalized in order to give an algorithm to find solutions of a linear partial differential equation at a singularity. The solutions found involve exponentials, logarithms and Laurent power series with exponents contained in a strongly convex cone.

We give a definition of Newton non degeneracy independent of the system of generators defining the variety. This definition extends the notion of Newton non degeneracy to varieties that are not necessarily complete intersection. As in the previous definition of non-degeneracy for complete intersection varieties, it is shown that the varieties satisfying our definition can be resolved with a toric modification. Using tools of both toric and tropical geometry we describe the toric modification in terms of the Groebner fan of the ideal defining the variety. The first part of the paper is devoted to introducing the classical concepts and the proof for the hypersurface case.

Inter-rater agreement is a crucial aspect in the planning and performance of a clinical trial in which the main assessment tool is the clinical interview. The main objectives of this study are to study the inter-rater agreement of a tool for the assessment of suicidal behavior (Brief Suicide Questionnaire) and to examine whether the inter-examiner agreement when multiple ratings are made on a single subject is an efficient method to assess the reliability of an instrument.In the context of designing a multicenter clinical trial, 32 psychiatrists assessed a videotaped clinical interview of a patient with suicidal behavior. In order to identify those items in which a greater level of discordance existed and detect the examiners whose ratings differed significantly from the average ratings, we used the DOMENIC method (Detecion of Multiple Examiners Not in Consensus).Inter-rater agreement was between poor (70%) to excelent (90-100%. Inter-rater agreement in Brugha's list of threatening experiences ranged from 75.5 and 100%; in the Global Assessment of Functioning (GAF) Scale was 82.58%; in the Beck's Suicidal Intent Scale, ranged from 67.5 and 97%; in the Beck's Scale for Suicide Ideation, ranged from 63.5 and 100%; and in the Lethality Rating Scale was 88.39%. On the whole, the level of agreement among raters, both in general scores and in particular items, was appropriate.The proposed design allows the assessment of the inter-rater agreement in an efficient way (only in one session). In addition, regarding the Brief Suicide Questionnaire, inter-raters agreement was appropriate.

We introduce a family of fields of series with support in strongly convex rational cones. All these fields contain the polynomials in several variables. We prove that they are algebraically closed with a construction that is analogous to the Newton polygon for algebraic curves. As a corollary we show the existence of fractional power solutions with support in cones for systems of equations

We give an algorithm to compute term by term multivariate Puiseux series expansions of series arising as local parametrizations of zeroes of systems of algebraic equations at singular points. The algorithm is an extension of Newton's method for plane algebraic curves replacing the Newton polygon by the tropical variety of the ideal generated by the system. As a corollary we deduce a property of tropical varieties of quasi-ordinary singularities., Comment: 19 pages. To appear in International Journal of Mathematics. Major changes: Several sections added explaining the geometrical meaning of the series solutions and a corollary about quasi-ordinary singularities

Given an N-dimensional germ of analytic hypersurface \( \mathcal{H} \), a finite projection π : \( \mathcal{H} \to \mathbb{C}^N \) and a valuation v on the ring of convergent series in N variables, we study the valuations on the ring \( \mathcal{O}_\mathcal{H} \) that extend π*v. All these valuations are described when v is a monomial valuation whose weight vector is not orthogonal to any of the faces of the Newton Polyhedron of the discriminant of the projection π. This description is done in terms of the Puiseux parameterizations of \( \mathcal{H} \) with exponents in a cone.

This paper describes an algorithmic method iterative method for searching power series solutions of a partial differential equation. Power series expansions considered have support in some convex cone of RN. We do this by introducing a N-variables analog of the Newton polygon construction, used in the case of ordinary 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.