Duality theory and slackness conditions in multiobjective linear programming

AbstractThe aim of this paper is to develop a duality theory for linear multiobjective programming verifying similar properties as in the scalar case. We use the so-called “strongly proper optima” and we characterize such optima and its associated dual solutions by means of some complementary slackness conditions. Moreover, the dual solutions can measure the sensitivity of the primal optima

Dating Clinopyroxene Phenocrysts in Submarine Basalts Using ^(40)Ar/^(39)Ar Geochronology

Dating submarine basalts using ^(40)Ar/^(39)Ar geochronology is often hindered by a lack of potassium‐bearing phenocrystic phases and severe alteration in the groundmass. Clinopyroxene is a common phenocrystic phase in seafloor basalts and is highly resistive to low‐temperature alteration. Here we show that clinopyroxene phenocrysts separated from marine basalts are a viable phase for ^(40)Ar/^(39)Ar incremental heating age determinations. We provide results from a pilot study comprising 16 age experiments from nine clinopyroxene separates, five of which from samples with dated coeval phases. The clinopyroxene ages range from 11.5 to 112 Ma with relatively high uncertainties (ranging from 0.8% to 7.1%; median of 1.9%) compared to more traditional phases. The clinopyroxene age plateaus form at low to moderate temperature steps and are characterized by relatively elevated K/Ca of 0.002–0.4, suggesting that other K‐bearing phases hosted within the clinopyroxene are likely degassing to yield the ^(40)Ar/^(39)Ar age information. There are three possible origins for the K and corresponding ^(40)Ar* including films of trapped melt/nanomineral inclusions along grain defects, secondary melt inclusion bands, or variations in degassing behaviors between lower and higher crystalline Ca pyroxene phases. Regardless of the source of the K, the age determinations are successful with 75% of the experiments producing long plateaus (>60% ^(39)Ar released) with mean square of the weighted deviations ranging from 0.6 to 1.5 and probability of fit values >0.05. We conclude that clinopyroxene dating by the ^(40)Ar/^(39)Ar method has the potential to provide a wealth of information for previously undated, altered seafloor lithologies and continental equivalents

Millennial-Scale Instability in the Geomagnetic Field Prior to the Matuyama-Brunhes Reversal

Changes in the Earth's magnetic field have global significance that reach from the outer core extending out to the uppermost atmosphere. Paleomagnetic records derived from sedimentary and volcanic sequences provide important insights into the geodynamo processes that govern the largest geomagnetic changes (polarity reversals), but dating uncertainties have hindered progress in this understanding. Here, we report a paleomagnetic record from multiple lava flows on Tahiti that bracket the Matuyama‐Brunhes (M‐B) polarity reversal ∼771,000 years ago. Our high‐precision ^(40)Ar/^(39)Ar ages constrain several rapid and short‐lived changes in field orientation up to 33,000 years prior to the M‐B reversal. These changes are similar to ones identified in other less well‐dated lava flows in Maui, Chile, and La Palma that occurred during an extended period of reduced field strength recorded in sediments. We use a simple stochastic model to show that these rapid polarity changes are highly attenuated in sediment records with low sedimentation rates. This prolonged 33,000 year period of reduced field strength and increased geomagnetic instability supports models that show frequent centennial‐to‐millennial‐scale polarity changes in the presence of a strongly weakened dipole field

New Insights into the Age and Origin of Two Small Cretaceous Seamount Chains Proximal to the Northwestern Hawaiian Ridge

The Northwestern Hawaiian Ridge is an age-progressive volcanic chain sourced from the Hawaiian mantle plume. Proximal to the Northwestern Hawaiian Ridge are several clusters of smaller seamounts and ridges with limited age constraints and unknown geodynamic origins. This study presents new bathymetric data and 40Ar/39Ar age determinations from lava flow samples recovered by remotely operated vehicle (ROV) from two east–west-trending chains of seamounts that lie north of the Pūhāhonu and Mokumanamana volcanoes. The previously unexplored Naifeh Chain (28°48′N,167°48′W) and Plumeria Chain (25°36′N, 164°35′W) contain five volcanic structures each, including three guyots in the Naifeh Chain. New 40Ar/39Ar age determinations indicate that the Naifeh Chain formed ca. 88 Ma and the Plumeria Chain ca. 85 Ma. The Cretaceous ages, coupled with a perpendicular orientation of the seamounts relative to absolute Pacific plate motion at that time, eliminate either a Miocene Hawaiian volcanic arch or Cretaceous mantle-plume origin. The seamounts lie on oceanic crust that is modeled to be 10–15 Ma older than the corresponding seamounts. Here, two models are put forth to explain the origin of these enigmatic seamount chains as well as the similar nearby Mendelssohn Seamounts. (1) Diffuse lithospheric extension results in the formation of these seamounts until the initiation of the Kula-Pacific spreading center in the north at 84–79 Ma, which alleviates the tension. (2) Shear-driven upwelling of enriched mantle material beneath young oceanic lithosphere results in an age-progressive seamount track that is approximately perpendicular to the spreading ridge. Here we show that all sampled seamounts proximal to the Northwestern Hawaiian Ridge are intraplate in nature, but their formations can be attributed to both plume and plate processes

Dating Clinopyroxene Phenocrysts in Submarine Basalts Using ^(40)Ar/^(39)Ar Geochronology

Dating submarine basalts using ^(40)Ar/^(39)Ar geochronology is often hindered by a lack of potassium‐bearing phenocrystic phases and severe alteration in the groundmass. Clinopyroxene is a common phenocrystic phase in seafloor basalts and is highly resistive to low‐temperature alteration. Here we show that clinopyroxene phenocrysts separated from marine basalts are a viable phase for ^(40)Ar/^(39)Ar incremental heating age determinations. We provide results from a pilot study comprising 16 age experiments from nine clinopyroxene separates, five of which from samples with dated coeval phases. The clinopyroxene ages range from 11.5 to 112 Ma with relatively high uncertainties (ranging from 0.8% to 7.1%; median of 1.9%) compared to more traditional phases. The clinopyroxene age plateaus form at low to moderate temperature steps and are characterized by relatively elevated K/Ca of 0.002–0.4, suggesting that other K‐bearing phases hosted within the clinopyroxene are likely degassing to yield the ^(40)Ar/^(39)Ar age information. There are three possible origins for the K and corresponding ^(40)Ar* including films of trapped melt/nanomineral inclusions along grain defects, secondary melt inclusion bands, or variations in degassing behaviors between lower and higher crystalline Ca pyroxene phases. Regardless of the source of the K, the age determinations are successful with 75% of the experiments producing long plateaus (>60% ^(39)Ar released) with mean square of the weighted deviations ranging from 0.6 to 1.5 and probability of fit values >0.05. We conclude that clinopyroxene dating by the ^(40)Ar/^(39)Ar method has the potential to provide a wealth of information for previously undated, altered seafloor lithologies and continental equivalents

Identification of the short-lived Santa Rosa geomagnetic excursion in lavas on Floreana Island (Galapagos) by ⁴⁰Ar/³⁹Ar geochronology

A set of closely related basaltic lava flows (supersite GA-X) on Floreana Island in the Galapagos Archipelago has a published record of an excursional or transitional direction (virtual geomagnetic pole located at 153.1°E, 54.2°S with α₉₅ = 5.0°) and a geomagnetic field strength (1.1 × 10²² Am²) that is only ∼14% of the strength of the modern magnetic field (7.8 × 10²² Am²). The very large age uncertainty of previous dating of a lava flow (G43) from this set, however, has prevented placing this event in the geomagnetic polarity time scale. Here we report highly reproducible and precise ⁴⁰Ar/³⁹Ar ages on the lava flow that indicate that the distinct geomagnetic excursion is 925.7 ± 4.6 ka (2σ; n = 6; mean square of weighted deviates = 1.23). This shows that this dramatic weakening of the geomagnetic field is associated with the Santa Rosa Excursion instead of the Matuyama-Brunhes polarity reversal. Our high-precision ⁴⁰Ar/³⁹Ar ages for Floreana provide evidence for the global significance of the Santa Rosa Excursion

Millennial-Scale Instability in the Geomagnetic Field Prior to the Matuyama-Brunhes Reversal

Changes in the Earth's magnetic field have global significance that reach from the outer core extending out to the uppermost atmosphere. Paleomagnetic records derived from sedimentary and volcanic sequences provide important insights into the geodynamo processes that govern the largest geomagnetic changes (polarity reversals), but dating uncertainties have hindered progress in this understanding. Here, we report a paleomagnetic record from multiple lava flows on Tahiti that bracket the Matuyama‐Brunhes (M‐B) polarity reversal ∼771,000 years ago. Our high‐precision ^(40)Ar/^(39)Ar ages constrain several rapid and short‐lived changes in field orientation up to 33,000 years prior to the M‐B reversal. These changes are similar to ones identified in other less well‐dated lava flows in Maui, Chile, and La Palma that occurred during an extended period of reduced field strength recorded in sediments. We use a simple stochastic model to show that these rapid polarity changes are highly attenuated in sediment records with low sedimentation rates. This prolonged 33,000 year period of reduced field strength and increased geomagnetic instability supports models that show frequent centennial‐to‐millennial‐scale polarity changes in the presence of a strongly weakened dipole field

Whole-genome sequencing of bladder cancers reveals somatic CDKN1A mutations and clinicopathological associations with mutation burden

Bladder cancers are a leading cause of death from malignancy. Molecular markers might predict disease progression and behaviour more accurately than the available prognostic factors. Here we use whole-genome sequencing to identify somatic mutations and chromosomal changes in 14 bladder cancers of different grades and stages. As well as detecting the known bladder cancer driver mutations, we report the identification of recurrent protein-inactivating mutations in CDKN1A and FAT1. The former are not mutually exclusive with TP53 mutations or MDM2 amplification, showing that CDKN1A dysfunction is not simply an alternative mechanism for p53 pathway inactivation. We find strong positive associations between higher tumour stage/grade and greater clonal diversity, the number of somatic mutations and the burden of copy number changes. In principle, the identification of sub-clones with greater diversity and/or mutation burden within early-stage or low-grade tumours could identify lesions with a high risk of invasive progression

Combining Enzalutamide with Abiraterone, Prednisone, and Androgen Deprivation Therapy in the STAMPEDE Trial

There are compelling reasons to study the addition of both enzalutamide and abiraterone, in combination, to standard-of-care for hormone-naïve prostate cancer. Through a protocol amendment, this will be assessed in the STAMPEDE trial, with overall survival as primary outcome measure. © 2014 European Association of Urology

A Novel Pzg-NURF Complex Regulates Notch Target Gene Activity

The Putzig (Pzg) protein is associated with the NURF nucleosome remodeling complex, thereby promoting Notch target gene expression. Our findings suggest a novel Pzg-NURF complex that is responsible for the epigenetic regulation of Notch target genes