An analysis of mixed integer linear sets based on lattice point free convex sets

Split cuts are cutting planes for mixed integer programs whose validity is derived from maximal lattice point free polyhedra of the form $S:=\{x : \pi_0 \leq \pi^T x \leq \pi_0+1 \}$ called split sets. The set obtained by adding all split cuts is called the split closure, and the split closure is known to be a polyhedron. A split set $S$ has max-facet-width equal to one in the sense that $\max\{\pi^T x : x \in S \}-\min\{\pi^T x : x \in S \} \leq 1$. In this paper we consider using general lattice point free rational polyhedra to derive valid cuts for mixed integer linear sets. We say that lattice point free polyhedra with max-facet-width equal to $w$ have width size $w$. A split cut of width size $w$ is then a valid inequality whose validity follows from a lattice point free rational polyhedron of width size $w$. The $w$-th split closure is the set obtained by adding all valid inequalities of width size at most $w$. Our main result is a sufficient condition for the addition of a family of rational inequalities to result in a polyhedral relaxation. We then show that a corollary is that the $w$-th split closure is a polyhedron. Given this result, a natural question is which width size $w^*$ is required to design a finite cutting plane proof for the validity of an inequality. Specifically, for this value $w^*$, a finite cutting plane proof exists that uses lattice point free rational polyhedra of width size at most $w^*$, but no finite cutting plane proof that only uses lattice point free rational polyhedra of width size smaller than $w^*$. We characterize $w^*$ based on the faces of the linear relaxation

\u3ci\u3eAcanthurus albimento\u3c/i\u3e, A New Species of Surgeonfish (Acanthuriformes: Acanthuridae) from Northeastern Luzon, Philippines, With Comments on Zoogeography

Acanthurus albimento is described as a new surgeonfish from northeastern Luzon from six specimens collected during extensive fish-market surveys in the Philippines. The new species is characterized by a distinctive white band below the lower jaw; many irregular, wavy, thin, blue lines on the head; a brown-orange pectoral fin with a bluish tinge on the outer membrane of the rays and a dark band on the posterior margin; a narrow rust-orange stripe along the base of the dorsal fin; and a large blackish caudal spine and sheath with the socket broadly edged in black. An analysis using the mitochondrial cytochrome c oxidase subunit 1 (COI), supported by an independent multi-locus analysis, suggests phylogenetic affinities with an Acanthurus clade that includes A. auranticavus, A. bariene, A. blochii, A. dussumieri, A. gahhm, A. leucocheilus, A. maculiceps, A. mata, A. nigricauda, and A. xanthopterus; a clade that shares a suite of color characteristics. Based on the sampling history in the region, the new species may be a limited-range endemic in the westernmost Pacific Ocean, which is unusual for members of this genus. This raises potential questions about drivers of dispersal and long-held assumptions about zoogeographic patterns along the Kuroshio Current

Disk Diffusion Propagation Model for the Outburst of XTE J1118+480

We present a linear diffusion model for the evolution of the double-peaked outburst in the transient source XTEJ1118+480. The model treats the two outbursts as episodic mass deposition at the outer radius of the disk followed by evolution of disk structure according to a diffusion process. We demonstrate that light curves with fast-rise, exponential decay profile are a general consequence of the diffusion process. Deconvolution of the light curve proves to be feasible and gives an input function specifying mass deposition at the outer disk edge as well as the total mass of the disk, both as functions of time. The derived evolution of total disk mass can be correlated with the observed evolution of the ~0.1 Hz QPO in the source reported in Wood et al. (2000).Comment: 26 pages, 6 figures, accepted for publication in Ap

Ginkgo leaf cuticle chemistry across changing pCO2 regimes

Cuticles have been a key part of palaeobotanical research since the mid-19th Century. Recently, cuticular research has moved beyond morphological traits to incorporate the chemical signature of modern and fossil cuticles, with the aim of using this as a taxonomic and classification tool. For this approach to work, cuticle chemistry would have to maintain a strong taxonomic signal, with a limited input from the ambient environment in which the plant grew. Here, we use attenuated total reflectance Fourier Transform infrared (ATR-FTIR) spectroscopy to analyse leaf cuticles from Ginkgo biloba plants grown in experimentally enhanced CO2 conditions, to test for the impact of changing CO2 regimes on cuticle chemistry. We find limited evidence for an impact of CO2 on the chemical signature of Ginkgo cuticles, with more pronounced differences demonstrated between the abaxial (lower leaf surface) and adaxial (upper leaf surface) cuticles. These findings support the use of chemotaxonomy for plant cuticular remains across geological timescales, and the concomitant large-scale variations in CO2 concentrations

Miocene magnetostratigraphy from Equatorial Pacific sediments (ODP Site 1218, Leg 199)

Pliocene and Miocene magnetostratigraphy from ODP Site 1218 (Equatorial Pacific) has been obtained by measurements made on u-channel samples, augmented by about 50 discrete samples. U-channel samples were measured at 1 cm intervals and stepwise demagnetized in alternating fields up to a maximum peak field of 80 mT. The component magnetization directions were determined by principal component analysis for demagnetization steps in the 20–60 mT peak field range. A relatively small number of discrete samples were subject to both thermal and alternating field (AF) demagnetization and gave results compatible with u-channel measurements. Magnetostratigraphy from u-channel samples are compared with shipboard data that were based on blanket demagnetization at peak AF fields of 20 mT. U-channel measurements add more detail to the magnetostratigraphic record and allow identification of thin polarity zones especially in the upper part of the section were the sedimentation rates are very low (∼2 m/Myr). The component magnetization directions determined from u-channel measurements also gave more reliable and precise estimates of inclination (paleolatitude). The magnetostratigraphy from Site 1218 can be unambiguously correlated with the reference geomagnetic polarity time scale and gives a means of dating the sedimentary sequence. Both Miocene–Pliocene and Oligocene–Miocene stage boundaries were easily identified from the magnetostratigraphic record. Although calculation of paleomagnetic poles is hindered by the low precision of the cores' azimuthal orientation, the data from both u-channel and discrete samples allow determination of the paleolatitude of the Site through time with good precision. Paleomagnetic data indicate that the paleolatitude of Site 1218 has increased form nearly equatorial latitude in the Oligocene to its present-day latitude close to 9°N. Within the precision of the paleomagnetic data, this is in agreement with current predictions of plate motion models based on fixed hotspots

Optical vernier technique for in-situ measurement of the length of long Fabry-Perot cavities

We propose a method for in-situ measurement of the length of kilometer size Fabry-Perot cavities in laser gravitational wave detectors. The method is based on the vernier, which occurs naturally when the laser incident on the cavity has a sideband. By changing the length of the cavity over several wavelengths we obtain a set of carrier resonances alternating with sideband resonances. From the measurement of the separation between the carrier and a sideband resonance we determine the length of the cavity. We apply the technique to the measurement of the length of a Fabry-Perot cavity in the Caltech 40m Interferometer and discuss the accuracy of the technique.Comment: LaTeX 2e, 12 pages, 4 figure

Using acoustic waves to induce high-frequency current oscillations in superlattices

We show that GHz acoustic waves in semiconductor superlattices can induce THz electron dynamics that depend critically on the wave amplitude. Below a threshold amplitude, the acoustic wave drags electrons through the superlattice with a peak drift velocity overshooting that produced by a static electric field. In this regime, single electrons perform drifting orbits with THz frequency components. When the wave amplitude exceeds the critical threshold, an abrupt onset of Bloch-like oscillations causes negative differential velocity. The acoustic wave also affects the collective behavior of the electrons by causing the formation of localised electron accumulation and depletion regions, which propagate through the superlattice, thereby producing self-sustained current oscillations even for very small wave amplitudes. We show that the underlying single-electron dynamics, in particular the transition between the acoustic wave dragging and Bloch oscillation regimes, strongly influence the spatial distribution of the electrons and the form of the current oscillations. In particular, the amplitude of the current oscillations depends non-monotonically on the strength of the acoustic wave, reflecting the variation of the single-electron drift velocity.Comment: 10 pages, 8 figure

Design report on the test system used to assess treatment of trench water from Waste Area Grouping 6 at Oak Ridge National Laboratory, Oak Ridge, Tennessee

New liquid waste streams will be generated as a consequence of closure activities at Waste Area Grouping (WAG) 6 at Oak Ridge National Laboratory (ORNL). It is proposed that these waste streams be treated for removal of contaminants by adding them to the ORNL wastewater treatment facilities. Previous bench-scale treatability studies indicate that ORNL treatment operations will adequately remove the contaminants, although additional study is required to characterize the secondary waste materials produced as a result of the treatment. A larger scale treatment system was constructed to produce secondary wastes in the quantities necessary for characterization and US Environmental protection Agency toxicity characteristic leaching procedure (TCLP) testing. The test system is designed to simulate the operation of the ORNL process waste treatment facilities and to treat a mixture of ORNL process wastewater and WAG 6 wastewater at a combined flow rate of 0.5 L/min. The system is designed to produce the necessary quantities of waste sludges and spent carbon for characterization studies and TCLP testing