Clustering Improves the Goemans–Williamson Approximation for the Max-Cut Problem

MAX−CUT is one of the well-studied NP-hard combinatorial optimization problems. It can be formulated as an Integer Quadratic Programming problem and admits a simple relaxation obtained by replacing the integer “spin” variables xi by unitary vectors v⃗ i. The Goemans–Williamson rounding algorithm assigns the solution vectors of the relaxed quadratic program to a corresponding integer spin depending on the sign of the scalar product v⃗ i⋅r⃗ with a random vector r⃗ . Here, we investigate whether better graph cuts can be obtained by instead using a more sophisticated clustering algorithm. We answer this question affirmatively. Different initializations of k-means and k-medoids clustering produce better cuts for the graph instances of the most well known benchmark for MAX−CUT. In particular, we found a strong correlation of cluster quality and cut weights during the evolution of the clustering algorithms. Finally, since in general the maximal cut weight of a graph is not known beforehand, we derived instance-specific lower bounds for the approximation ratio, which give information of how close a solution is to the global optima for a particular instance. For the graphs in our benchmark, the instance specific lower bounds significantly exceed the Goemans–Williamson guarantee

Resultados del tratamiento quirúrgico del dolor lumbar con instrumentación diapasón

Se presenta un estudio sobre 23 pacientes con patología lumbosacra tratados quirúrgicamente mediante artrodesis e instrumentación vertebral transpedicular tipo diapasón. El promedio de seguimiento ha sido de 25 meses (18-38). El dolor lumbar estaba relacionado en 10 casos con estenosis de canal, en 6 con espondilolistesis y en 7 con hernia discal y artrosis secundaria. Todos fueron instrumentados por vía posterior mediante fijación transpedicular y artrodesados posterolateralmente con injerto autólogo. Se consiguió una artrodesis sólida en un 96%. No se han presentado complicaciones preoperatorias. Ocho pacientes presentaron complicaciones en el postoperatorio inmediato. Observamos un desplazamiento de barra y un desanclaje del tornillo fuera del pedículo. Siguiendo los criterios de valoración de Henderson se ha conseguido un 96% de excelentes y buenos resultados.A series of 23 patient with lumbosacral pathology, surgically treated by posterior arthrodesis and vertebral diapason transpedicular fixation was retrospectively review. The average follow-up period was 25 months (18-38). The diagnosis was spinal stenosis in 10 cases, spondylolisthesis in 6, and disc herniation with secondary osteoartrhitis in 7 cases. Apart from transpedicular fixation all cases underwent posterolateral fusion with autogenous bone graft. A solid arthrodesis was achieved in a 96% of patients. There were no per-operative complication. Eight cases showed complications in the immediate postoperative period. We observed displacement of a bar and detachement of a screw out off the pedicle. According to Henderson's assessment criteria we obtained 96% of excellent and good results

The halo white dwarf population

Halo white dwarfs can provide important information about the properties and evolution of the galactic halo. In this paper we compute, assuming a standard IMF and updated models of white dwarf cooling, the expected luminosity function, both in luminosity and in visual magnitude, for different star formation rates. We show that a deep enough survey (limiting magnitude > 20) could provide important information about the halo age and the duration of the formation stage. We also show that the number of white dwarfs produced using the recently proposed biased IMFs cannot represent a large fraction of the halo dark matter if they are constrained by the presently observed luminosity function. Furthermore, we show that a robust determination of the bright portion of the luminosity function can provide strong constraints on the allowable IMF shapes.Comment: 29 pages (AASTeX), 7 eps figures included, accepted for publication in Ap

Mind the Gap: Computing Finance-Neutral Output Gaps in Latin-American Economies

We compute a measure of the finance-neutral potential output for Colombia, Chile and Mexico. Our methodology is based on Borio et al (2013, 2014) and incorporates the cycle of credit, house prices and the real exchange rate on the computation of the output gap. The literature on business cycles in emerging market economies, particularly papers focusing on Latin American economies, has highlighted the importance of including shocks to the interest rate in world capital markets together with financial frictions; terms of trade fluctuations; and a procyclical government spending process. Our results show that around the financial crises of the 1990s the finance-neutral output gap behaved differently than the traditional measures observed by policymakers. In particular, gaps are higher before crises and lower after them

First bounds on the high-energy emission from isolated Wolf-Rayet binary systems

High-energy gamma-ray emission is theoretically expected to arise in tight binary star systems (with high mass loss and high velocity winds), although the evidence of this relationship has proven to be elusive so far. Here we present the first bounds on this putative emission from isolated Wolf-Rayet (WR) star binaries, WR 147 and WR 146, obtained from observations with the MAGIC telescope.Comment: (Authors are the MAGIC Collaboration.) Manuscript in press at The Astrophysical Journal Letter

Plan de negocio para la implementaci?n de registro digital de documentaci?n notarial utilizando tecnolog?a Blockchain

El plan de negocio que se desarrolla en el presente proyecto de tesis, es sobre una plataforma tecnol?gica basada en blockchain para el registro de documentos notariales ofreciendo caracter?sticas como integridad, seguridad, inmutabilidad, accesibilidad y visibilidad. De esta manera las notar?as, mediante esta plataforma, brindar?n a sus clientes una alternativa digital con la misma validez que el documento f?sico. Asimismo, esta alternativa les significar?a una fuente de ingresos y un valor agregado a los servicios notariales que actualmente son ofrecidos en este mercado. Debido que el sector notarial de Lima Metropolitana busca una evoluci?n en sus servicios actuales, se realiz? una investigaci?n de mercado y entrevistas a expertos tecnol?gicos en blokchain, desarrollando una propuesta de modelo de negocio que aprovecha las caracter?sticas tecnol?gicas del blockchain para ofrecer un valor de diferenciaci?n a los usuarios finales, a su vez realizando un an?lisis del mercado actual y su desarrollo. Siendo la tecnolog?a propuesta una alternativa superior a otras actuales como la firma digital, todo esto para evitar problemas como la falsificaci?n de documentos o delitos contra la fe p?blica. Sirviendo este documento como referencia para estudios en el sector notarial peruano y a nivel tecnol?gico para nuevos modelos de negocio utilizando tecnolog?as disruptivas

Observation of Pulsed Gamma-rays Above 25 GeV from the Crab Pulsar with MAGIC

One fundamental question about pulsars concerns the mechanism of their pulsed electromagnetic emission. Measuring the high-end region of a pulsar's spectrum would shed light on this question. By developing a new electronic trigger, we lowered the threshold of the Major Atmospheric gamma-ray Imaging Cherenkov (MAGIC) telescope to 25 GeV. In this configuration, we detected pulsed gamma-rays from the Crab pulsar that were greater than 25 GeV, revealing a relatively high cutoff energy in the phase-averaged spectrum. This indicates that the emission occurs far out in the magnetosphere, hence excluding the polar-cap scenario as a possible explanation of our measurement. The high cutoff energy also challenges the slot-gap scenario.Comment: Slight modification of the analysis: Fitting a more general function to the combined data set of COMPTEL, EGRET and MAGIC. Final result and conclusion is unchange

Probing quantum gravity using photons from a flare of the active galactic nucleus Markarian 501 observed by the MAGIC telescope

We analyze the timing of photons observed by the MAGIC telescope during a flare of the active galactic nucleus Mkn 501 for a possible correlation with energy, as suggested by some models of quantum gravity (QG), which predict a vacuum refractive index \simeq 1 + (E/M_{QGn})^n, n = 1,2. Parametrizing the delay between gamma-rays of different energies as \Delta t =\pm\tau_l E or \Delta t =\pm\tau_q E^2, we find \tau_l=(0.030\pm0.012) s/GeV at the 2.5-sigma level, and \tau_q=(3.71\pm2.57)x10^{-6} s/GeV^2, respectively. We use these results to establish lower limits M_{QG1} > 0.21x10^{18} GeV and M_{QG2} > 0.26x10^{11} GeV at the 95% C.L. Monte Carlo studies confirm the MAGIC sensitivity to propagation effects at these levels. Thermal plasma effects in the source are negligible, but we cannot exclude the importance of some other source effect.Comment: 12 pages, 3 figures, Phys. Lett. B, reflects published versio

Simultaneous multi-frequency observation of the unknown redshift blazar PG 1553+113 in March-April 2008

The blazar PG 1553+113 is a well known TeV gamma-ray emitter. In this paper, we determine its spectral energy distribution using simultaneous multi-frequency data in order to study its emission processes. An extensive campaign was carried out between March and April 2008, where optical, X-ray, high-energy (HE) gamma-ray, and very-high-energy (VHE) gamma-ray data were obtained with the KVA, Abastumani, REM, RossiXTE/ASM, AGILE and MAGIC telescopes, respectively. This is the first simultaneous broad-band (i.e., HE+VHE) gamma-ray observation, though AGILE did not detect the source. We combine data to derive source's spectral energy distribution and interpret its double peaked shape within the framework of a synchrotron self compton modelComment: 5 pages, 2 figures, publishe