Detecting optimality and extracting solutions in polynomial optimization with the truncated GNS construction

A basic closed semialgebraic subset of $\mathbb{R}^{n}$ is defined by simultaneous polynomial inequalities $p_{1}\geq 0,\ldots,p_{m}\geq 0$. We consider Lasserre's relaxation hierarchy to solve the problem of minimizing a polynomial over such a set. These relaxations give an increasing sequence of lower bounds of the infimum. In this paper we provide a new certificate for the optimal value of a Lasserre relaxation be the optimal value of the polynomial optimization problem. This certificate is that a modified version of an optimal solution of the Lasserre relaxation is a generalized Hankel matrix. This certificate is more general than the already known certificate of an optimal solution being flat. In case we have optimality we will extract the potencial minimizers with a truncated version of the Gelfand-Naimark-Segal construction on the optimal solution of the Lasserre relaxation. We prove also that the operators of this truncated construction commute if and only if the matrix of this modified optimal solution is a generalized Hankel matrix. This generalization of flatness will bring us to reprove a result of Curto and Fialkow on the existence of quadrature rule if the optimal solution is flat and a result of Xu and Mysovskikh on the existance of a Gaussian quadrature rule if the modified optimal solution is generalized Hankel matrix. At the end, we provide a numerical linear algebraic algorithm for dectecting optimality and extracting solutions of a polynomial optimization problem

Mechanisms and strategies for promotion, rise and consolidation of the Carrillo de Toledo, Lords of Caracena and Pinto

Como ha sido puesto de manifiesto ya en reiteradas ocasiones la movilidad social fue un fenómeno característico del sistema estamental propio de la Edad Moderna. El dinero fue un elemento clave en el intento por conseguir la ansiada promoción, como también esencial fue saber aprovechar las oportunidades de servicio regio que brindó la maquinaria imperial de los Austrias. En el proceso de encumbramiento político y social protagonizado por los señores de Caracena y Pinto, la concesión del señorío, el acceso a las esferas locales de gobierno, la fundación de mayorazgos, la puesta en práctica de unas acertadas estrategias matrimoniales y, finalmente, el desempeño de algunos de los puestos administrativos, gubernativos y militares más relevantes de la Monarquía Hispánica, se convirtieron en hitos fundamentales. Trayectoria ascendente, por tanto, la de estos señores, que les permitió, además, acumular honores y mercedes, diversificar sus fuentes de ingresos, apuntalar un estatus privilegiado y entrar a formar parte de la nobleza titulada.Social mobility was a typical phenomenon in the estates system of the Modern Age, as it has already been shown repeatedly. Money was a key element in an attempt to get the coveted promotion as well as to seize opportunities for royal service that the Habsburg imperial machinery provided. In the political and social elevation process starred by the lords of Caracena and Pinto, the grant of the manor, the access to government local areas, the foundation of “mayorazgos”, the implementation of some successful marriage strategies, and finally, the performance of some of the most relevant administrative, governmental and military positions of the Spanish monarchy became milestones. Therefore, these lords’ upward career also allowed them to build up honors and rewards, diversify their income sources, as well as prop up a privileged status and become part of the titled nobility

Impact of bonfires on soil properties in an urban park in Vilnius (Lithuania)

Lighting bonfires in urban parks is a widespread practice. However, few studies have examined their impact on soil properties. The aim of this study was to analyze the impact of bonfires on the soil properties of an urban park in Vilnius, Lithuania. The properties studied were soil water repellency (SWR), aggregate stability (AS), soil organic matter (SOM) content, total nitrogen (TN), inorganic carbon (IC), pH, electrical conductivity (EC), extractable calcium (Ca), magnesium (Mg), sodium (Na), potassium (K), aluminum (Al), manganese (Mn), iron (Fe), zinc (Zn), copper (Cu), boron (B), chromium (Cr), available phosphorus (P), silicon (Si) and sulfur (S). Soil ratios calculated were carbon/nitrogen ratio (C/N), Ca+Mg/(Na+K)1/2 (SPAR), Ca:Al and Ca:Mg. Three areas were studied: Site 1) Pinus sylvestris L. and Quercus robur L.; Site 2) Aesculus glabra Wild.; and Site 3) Pinus sylvestris L. and Acer plantanoides L. At each site, 20 samples were collected (10 within the bonfire area, 10 from a control area). The results showed significantly higher values of SOM, IC, pH, EC, Ca, Mg, Na, K, P, Al, Zn, Cu, Cr, S, C/N ratio, Ca:Al ratio and Ca:Mg ratio in bonfire soils than in control unburned soils. In bonfire soils, significantly lower values were recorded of SWR, AS, TN, SOM, Al, Mn, Fe, Cr, S and SPAR comparing to control soils. Most affected area by the bonfire was Site 1, which presented a marked increase in heavy metal content comparing to the control. The impact of soil heating was evident in AS, IC, pH, extractable Ca, Mg, Na, K, P, Al, Zn, Cu, Cr, S, and in its ratios. Protective measures are needed to limit bonfires and prohibit the burning of hazardous materials

A multi-ion beam microanalysis approach for the characterization of plasma polymerized allylamine films

EPJ Applied Physics 56. 2 (2011): 24021 with kind permission of The European Physical Journal (EPJ)A full characterization of plasma polymerized biofunctional films requires the use of multi-analytical approaches to determine the chemical composition, topography and potential interaction mechanisms of such films with biomolecules and cells. In this work we aim at underlining the versatility of ion-based techniques to contribute to the chemical characterization of plasma polymerized surfaces. The simultaneous use of energy recoil detection (ERD) and Rutherford backscattering (RBS) spectroscopies with incident He ions is an example of this versatility. Performing sequential measurements and the use of correlating computing tools for ERD-RBS interpretation allows providing in-depth concentration profiles of light elements, including namely hydrogen. More accurate analysis of light elements in polymer films can be increased by looking for particular ions with resonant backscattering responses (i.e., non-Rutherford Scattering). In particular, proton beams of 1.765 MeV are used to increase the detection of C and N, and particular incidence and detector angles to diminish the Si substrate contribution. These analytical tools have been applied to allylamine films and multi-layers crosslinked in a capacitive plasma onto both Si and porous Si substratesWe acknowledge MICINN funding provided by Grant No. MAT2008-06858-C02-01 and grant from Fundación Domingo Martíne

Effect of pre- and post-wildfire management practices on plant recovery after a wildfire in Northeast Iberian Peninsula

[En] Fire and pre- or post-fire management practices shape the distribution and richness of plant species. Here, the effects of pre- and post-fire management on vegetation recovery were studied at different times, up to 18 months after a wildfire. Two months after a 2015 wildfire, 18 study plots were established (three 4-m2 plots for each treatment), vegetation regrowth was monitored and vegetal species richness (S), evenness (IT), density (D), diversity (H0) and maximum diversity (HMax) after 2, 10 and 18 months. The treatments were (1) control, unaffected by 2015 wildfire; (2) no treatment (NT), burned in 2015 wildfire and not managed; (3) managed in 2005 and burned in 2015 (M05B); (4) managed in 2015, 2 months before wildfire (M15B); (5) cut and manual removal after the 2015 wildfire (CR); (6) cut and no trunk removal randomly deposited on topsoil after the 2015 wildfire (CL). All the treatments were carried out in a Pinus halepensis Miller forest. At 10 and 18 months after the wildfire, vegetation recovery was greater in NT, CR and CL plots than in M05B and M15B the plots. By 18 months after the wildfire, Brachypodium retusum (Pers.) P. Beauv. and Rosmarinus officinalis L. were still dominant, especially in M15B, corroborating the belief that pre-fire treatment reduced ecosystem resilience and vegetal recovery compared to the NT and post-fire managed plots. Richness was significantly lower 10 months after wildfire in control plots, and IT was significantly higher in that inventory than previously in M15B. Eighteen months after the wildfire, H0 was significantly lower in M15B. Ten months post-wildfire, HMax was significantly lower in the control plots. Eighteen months after the wildfire, HMax, was significantly higher in CR, CL and M05B than in the control and M15B plots. Overall, pre-fire management was detrimental to post-fire vegetation recovery, while manual post-fire management proved beneficial

Characterisation of the sintering behaviour of Waelz slag from electric arc furnace (EAF) dust recycling for use in the clay ceramics industry

Waelz slag is an industrial by-product from the recovery of electric arc furnace (EAF) dust which is mainly sent to landfills. Despite the different chemical and mineralogical compositions of Waelz slag compared to traditional clays, previous experiments have demonstrated its potential use as a clay substitute in ceramic processes. Indeed, clayey products containing Waelz slag could improve mechanical and environmental performance, fixing most of the metallic species and moreover decreasing the release of some potential pollutants during firing. However, a deeper understanding of the complex phase transformations during its thermal treatment and the connection of this behaviour with the end properties is desirable in order to explain the role that is played by the Waelz slag and its potential contribution to the ceramic process. For this purpose, in the present study, the chemical, mineralogical, thermal and environmental behaviour of both (i) unfired powdered samples, and (ii) pressed specimen of Waelz slag fired up to different temperatures within the typical range of clay based ceramic production, has been studied. The effect of the heating temperature on the end properties of the fired samples has been assessed. In general, an increase of the firing temperature promotes sintering and densification of the products and decreases the open porosity and water absorption which also contributes to the fixation of heavy metals. On the contrary, an increase in the leaching of Pb, Cr and Mo from the fired specimens is observed. This can be attributed to the creation of Fe and Ca molybdates and chromates that are weakly retained in the alkali matrix. On the other side, at temperature above 950 °C a weight gain related to the emission of evolved gases is observed. In conclusion, the firing temperature of the ceramic process is a key parameter that affects not only the technical properties but also strongly affects the leaching behaviour and the process emissions.The authors gratefully acknowledge the financial support for this research by the BEFESA STEEL R&D, S.L.U. Company, Erandio, Biscay (España) and the framework of the Spanish Ministry of Science and Innovation Project (CTM 2009-11303 TECNO).Peer reviewe

Sistemes de gestió de continguts i Wordpress : les claus del sector

Els Sistemes de Gestió de Continguts, o CMS, estan augmentant la seva presència al mercat d'una forma molt destacada en els últims anys. Cada vegada són més les empreses i particulars que han decidit apostar per aquest tipus de frameworks per a implementar els seus llocs i plataformes web. L'objectiu essencial d'aquest projecte és arribar a les autèntiques raons d'aquest moviment, conèixer a fons com es treballa amb aquest tipus d'eina i demostrar si el potencial del que presumeixen és real o no. Per aconseguir-ho es realitzaran diversos estudis teòrics propis on s'analitzaran les funcionalitats i requeriments dels CMS més utilitzats al mercat i paral·lelament com a part pràctica del projecte, s'implementarà una eina e-learning i una altre e-commerce amb un Sistema de Gestió de Continguts escollit amb les que s'intentarà arribar a un nivell funcional idèntic al que proporcionen plataformes especialitzades en aquests dos sectors.The Content Management System, or CMS, are increasing their market presence in a very prominent in recent years. More and more companies and individuals who have decided to opt for this type of frameworks to implement their web sites and platforms. The main objective of this project is to reach the real reasons for this movement, get to know how to work with this type of tool and show if the potential is real or not". Consequently, several theoretical studies conducted themselves on analyzing the features and requirements of the most used CMS in the market and parallel practice as part of the project, implemented an e-learning tool and another with e-commerce a content management system chosen that try to reach a functional level identical to that provide specialized platforms in these two sectors.Los Sistemas de Gestión de Contenidos o CMS están aumentado su presencia en el mercado de una forma destacada en los últimos años. Cada vez son más las empresas y particulares que han decidido apostar por este tipo de frameworks para implementar sus sitios y plataformas web. El objetivo esencial de este proyecto es llegar a las auténticas razones de este movimiento, conocer a fondo como se trabaja con este tipo de herramienta y demostrar si el potencia del que presumen es real o no. Para conseguirlo se realizarán diversos estudios teóricos propios donde se analizarán las funcionalidades y requisitos de los CMS más utilizados actualmente en el mercado y paralelamente, como parte práctica del proyecto, se implementará una herramienta e-learning y otra e-commerce con un Sistema de Gestión de Contenidos elegido con las que se intentará llegar a un nivel funcional idéntico al que proporcionan plataformas especializadas en estos dos sectores

Mecanismos y estrategias de promoción, ascenso y consolidación de los Carrillo de Toledo, señores de Caracena y Pinto

Social mobility was a typical phenomenon in the estates system of the Modern Age, as it has already been shown repeatedly. Money was a key element in an attempt to get the coveted promotion as well as to seize opportunities for royal service that the Habsburg imperial machinery provided. In the political and social elevation process starred by the lords of Caracena and Pinto, the grant of the manor, the access to government local areas, the foundation of “mayorazgos”, the implementation of some successful marriage strategies, and finally, the performance of some of the most relevant administrative, governmental and military positions of the Spanish monarchy became milestones. Therefore, these lords’ upward career also allowed them to build up honors and rewards, diversify their income sources, as well as prop up a privileged status and become part of the titled nobility.Como ha sido puesto de manifiesto ya en reiteradas ocasiones la movilidad social fue un fenómeno característico del sistema estamental propio de la Edad Moderna. El dinero fue un elemento clave en el intento por conseguir la ansiada promoción, como también esencial fue saber aprovechar las oportunidades de servicio regio que brindó la maquinaria imperial de los Austrias. En el proceso de encumbramiento político y social protagonizado por los señores de Caracena y Pinto, la concesión del señorío, el acceso a las esferas locales de gobierno, la fundación de mayorazgos, la puesta en práctica de unas acertadas estrategias matrimoniales y, finalmente, el desempeño de algunos de los puestos administrativos, gubernativos y militares más relevantes de la Monarquía Hispánica, se convirtieron en hitos fundamentales. Trayectoria ascendente, por tanto, la de estos señores, que les permitió, además, acumular honores y mercedes, diversificar sus fuentes de ingresos, apuntalar un estatus privilegiado y entrar a formar parte de la nobleza titulada

Hard & Soft flexibility: [Des]montando la vivienda

Després de tant de temps tancats a casa per la pandèmia, la societat espanyola va ser conscient que els seus habitatges no s'adaptaven a les necessitats. I les dades , demolidores, van corroborar tota sospita: el parc immobiliari espanyol, a més d'envellit, estava quedant obsolet. Davant aquesta situació alarmant, arquitectes, constructores i promotores hem de respondre amb celeritat, per solucionar el problema d'origen i evitar que en unes dècades la societat hagi de tornar a enfrontar-se a aquest mateix problema. Una de les alternatives: l'ús de larquitectura flexible. Serà la millor solució? Aquesta i moltes més incògnites seran resoltes en aquest treball de recerca i estudi.Tras tanto tiempo encerrados en casa por la pandemia, la sociedad española fue consciente de que sus viviendas no se adaptaban a sus necesidades. Y los datos , demoledores, corroboraron toda sospecha: el parque inmobiliario español, además de envejecido, estaba quedando obsoleto. Ante esta situación alarmante, arquitectos, constructores y promotores hemos de responder con celeridad, para solucionar el problema de raíz y evitar que en unas décadas la sociedad deba volver a enfrentarse a este mismo problema. Una de las alternativas: el uso de la arquitectura flexible. ¿Será la mejor solución? Esta y muchas más incógnitas buscarán ser resueltas en este trabajo de investigación y estudio.After so much time locked up at home due to the pandemic, Spanish society was aware that their homes were not adapted to their needs. And the data, devastating, corroborated all suspicions: the Spanish real estate stock, in addition to being old, was becoming obsolete. Faced with this alarming situation, architects, builders and promoters have to respond quickly, to solvethe root problem and prevent society from having to face this same problem again in a few decades. One of the alternatives: the use of flexible architecture. Will it be the best solution? This and many more unknowns will seek to be resolved in this research and study work

Differential effects on KCC2 expression and spasticity of ALS and traumatic injuries to motoneurons

Amyotrophic lateral sclerosis (ALS) is a neurodegenerative disease manifested by progressive muscle atrophy and paralysis due to the loss of upper and lower motoneurons (MN). Spasticity appears in ALS patients leading to further disabling consequences. Loss of the inhibitory tone induced by downregulation of the potassium chloride cotransporter 2 (KCC2) in MN has been proposed to importantly contribute to the spastic behavior after spinal cord injury (SCI). The aim of the present study was to test whether the alterations in the expression of KCC2 are linked to the appearance of spasticity in the SOD(G93A) ALS murine model. We compared SOD(G93A) mice to wild type mice subjected to SCI to mimic the spinal MN disconnection from motor descending pathways, and to sciatic nerve lesion to mimic the loss of MN connectivity to muscle. Electrophysiological results show that loss of motor function is observed at presymptomatic stage (8 weeks) in SOD(G93A) mice but hyperreflexia and spasticity do not appear until a late stage (16 weeks). However, KCC2 was not downregulated despite MN suffered disconnection both from muscles and upper MNs. Further experiments revealed decreased gephyrin expression, as a general marker of inhibitory systems, accompanied by a reduction in the number of Renshaw interneurons. Moreover, 5-HT fibers were increased in the ventral horn of the lumbar spinal cord at late stage of disease progression in SOD1(G93A) mice. Taken together, the present results indicate that spasticity appears late in the ALS model, and may be mediated by a decrease in inhibitory interneurons and an increase of 5-HT transmission, while the absence of down-regulation of KCC2 could rather indicate an inability of MNs to respond to insult