On the local stability of semidefinite relaxations

We consider a parametric family of quadratically constrained quadratic programs (QCQP) and their associated semidefinite programming (SDP) relaxations. Given a nominal value of the parameter at which the SDP relaxation is exact, we study conditions (and quantitative bounds) under which the relaxation will continue to be exact as the parameter moves in a neighborhood around the nominal value. Our framework captures a wide array of statistical estimation problems including tensor principal component analysis, rotation synchronization, orthogonal Procrustes, camera triangulation and resectioning, essential matrix estimation, system identification, and approximate GCD. Our results can also be used to analyze the stability of SOS relaxations of general polynomial optimization problems.Comment: 23 pages, 3 figure

Cool dwarfs in wide multiple systems. Paper 6: A curious quintuple system of a compact Sun-like triple and a close pair of an M dwarf and a very cool white dwarf at a wide separation

The system WDS 16329+0315 is an old, nearby quintuple physical system in the thick Galactic disc formed by a close-resolved, triple primary of solar metallicity, namely HD 149162, and a very wide, common proper motion, secondary pair, formed by the mid-M dwarf G-17-23 and the white dwarf LSPM J1633+0311S. We present an exhaustive astrometric and photometric data compilation of the system, including Gaia DR2 parallaxes and proper motions, and the first analysis of the nature of the faintest component. LSPM J1633+0311S (HD 149162 C) is a very cool white dwarf with an effective temperature of only about 5500 K, near the coolest end of the grid of theoretical models.Comment: The Observatory, in press, to appear in December 201

Hospitalización por episodios de cianosis en recién nacidos de edad gestacional igual o mayor a 34 semanas

ResumenObjetivoCaracterizar la hospitalización por episodios de cianosis en recién nacidos (RN)>34semanas.Pacientes y métodoEstudio retrospectivo que incluyó la totalidad de los RN hospitalizados por episodios de cianosis entre enero de 2007 y diciembre de 2012. En ellos se aplicaron 2 protocolos de estudio que consideraban exámenes de primera y segunda línea; estos últimos ante la recurrencia de eventos. El protocolo de primera línea consideró exámenes bioquímicos generales, radiografía de tórax y ecocardiografía en casos seleccionados, en tanto que el protocolo de segunda línea incluyó electroencefalograma, electrocardiograma, resonancia magnética nuclear encefálica, screening metabólico ampliado, ácido pirúvico, ácido láctico y en caso de convulsiones, citoquímico y cultivo de líquido cefalorraquídeo y reacción en cadena de la polimerasa para herpes.ResultadosNoventa y ocho de un total de 3.454 (2,8%) RN hospitalizados ingresaron por episodio de cianosis. La edad gestacional (EG) fue 37,8+1,36 semanas; peso al nacimiento: 3145+477g. Edad materna: 32+4,8 años. El 19,4% de las madres tenía antecedentes mórbidos: diabetes gestacional (8,1%), síndrome hipertensivo del embarazo (5,1%), colestasia intrahepática (3,1%) y retardo del crecimiento (3,1%). Género: 48,8% masculino, parto por cesárea: 68,4%. Edad al ingreso: 1,9+1,4 días; duración de la hospitalización: 4,2+4,2 días. En todos los pacientes se practicaron exámenes de primera línea y en el 39,8% exámenes de segunda línea. En el 21,4% de los RN se identificó una causa, siendo el síndrome convulsivo el más frecuente (33%). Los RN con diagnóstico asociado presentaron 3,8+2,7 episodios de cianosis versus 1,5+2,4 en el grupo sin diagnóstico (NS). El 15,4% se fueron de alta con monitor; no hubo reingresos.ConclusiónLa incidencia de hospitalización neonatal por episodios de cianosis fue de 6 por 1.000 RN vivos. Solo en cerca de un 20% de ellos es posible identificar una causa, siendo la más frecuente el síndrome convulsivo.AbstractObjectivesA retrospective study was performed between January 2007 and December 2012 to assess the admission rates of newborns due to episodes of cyanosisPatients and methodRetrospective study that included all the newborns hospitalized with episodes of cyanosis between January 2007 and December 2012. In them were employed two study protocols that considered first and second line tests, the latter in view of recurrence of events. The first line protocol considered general biochemical tests, chest x-ray and echocardiography in selected cases, while the second line protocol included electroencephalogram, electrocardiogram, nuclear magnetic resonance of the brain, expanded metabolic screening, pyruvic acid, lactic acid, and in case of seizures, cytochemical, and culture of cerebrospinal fluid (CSF) and PCR (polymerase chain reaction) for herpes.ResultsA total of 98 (2.8%) out of 3,454 newborns were admitted due to episodes of cyanosis. Gestational age: 37.8+1.4 weeks, birth weight: 3,145+477g. Maternal age: 32+4.8 years. Disease was present in 19.4% of mothers; gestational diabetes (8.1%), pregnancy induced hypertension (5.1%), intrahepatic cholestasis (3.1%), and intrauterine growth retardation (3.1%). Gender: 48.8% male, 51.2% female (NS). Birth: caesarean section, 68.4%, and vaginal delivery, 31.6%. Age on admission 1.9+1.4 days. Hospital stay: 4.2+4.2 days. First line tests were performed in 100% of patients with 39.8% fulfilling the criteria for second line study. A condition was detected in 21.4%, with convulsive syndrome was the most frequent (33%). Newborns with an identified condition had 3.8+2.7episodes versus 1.5+2,4 in those without diagnosis (NS). A home oxygen monitor was given to 15.4%. There were no re-admissions.ConclusionsMost newborns admitted due to cyanosis are discharged with a condition of unknown origin. In this study, convulsive syndrome was the most frequent cause

RELIABILITY OF LOW-COST PORTABLE FORCE PLATFORMS FOR MEASURING VERTICAL STIFFNESS DURING RUNNING

Ground reaction force (GRF) can provide useful information such as vertical stiffness (Kvert) to practitioners working with runners and sprinters, but high equipment costs are hindering applied research. Low-cost portable force platforms may be a useful alternative to traditional biomechanical equipment. Moderately trained runners (n = 9) completed overground running trials at various speeds (2.15-5.78 m/s), Kvert was determined, and a linear regression was used to characterize the relationship between Kvert and running speed. The results showed moderate to high correlation (r2 = 0.54 to 0.87). At 3.9 m/s (14 km/h), the widest regression model confidence interval was 4.4%, which shows this procedure likely provides adequate reliability. Future research should continue to investigate the use of low-cost portable force platforms for measuring running GRF