Splitting Proofs for Interpolation

We study interpolant extraction from local first-order refutations. We present a new theoretical perspective on interpolation based on clearly separating the condition on logical strength of the formula from the requirement on the com- mon signature. This allows us to highlight the space of all interpolants that can be extracted from a refutation as a space of simple choices on how to split the refuta- tion into two parts. We use this new insight to develop an algorithm for extracting interpolants which are linear in the size of the input refutation and can be further optimized using metrics such as number of non-logical symbols or quantifiers. We implemented the new algorithm in first-order theorem prover VAMPIRE and evaluated it on a large number of examples coming from the first-order proving community. Our experiments give practical evidence that our work improves the state-of-the-art in first-order interpolation.Comment: 26th Conference on Automated Deduction, 201

Star cluster ecology IVa: Dissection of an open star cluster---photometry

The evolution of star clusters is studied using N-body simulations in which the evolution of single stars and binaries are taken self-consistently into account. Initial conditions are chosen to represent relatively young Galactic open clusters, such as the Pleiades, Praesepe and the Hyades. The calculations include a realistic mass function, primordial binaries and the external potential of the parent Galaxy. Our model clusters are generally significantly flattened in the Galactic tidal field, and dissolve before deep core collapse occurs. The binary fraction decreases initially due to the destruction of soft binaries, but increases later because lower mass single stars escape more easily than the more massive binaries. At late times, the cluster core is quite rich in giants and white dwarfs. There is no evidence for preferential evaporation of old white dwarfs, on the contrary the formed white dwarfs are likely to remain in the cluster. Stars tend to escape from the cluster through the first and second Lagrange points, in the direction of and away from the Galactic center. Mass segregation manifests itself in our models well within an initial relaxation time. As expected, giants and white dwarfs are much more strongly affected by mass segregation than main-sequence stars. Open clusters are dynamically rather inactive. However, the combined effect of stellar mass loss and evaporation of stars from the cluster potential drives its dissolution on a much shorter timescale than if these effects are neglected. The often-used argument that a star cluster is barely older than its relaxation time and therefore cannot be dynamically evolved is clearly in error for the majority of star clusters.Comment: reduced abstract, 33 pages (three separate color .jpg figures), submitted to MNRA

Kinematical fingerprints of star cluster early dynamical evolution

We study the effects of the external tidal field on the violent relaxation phase of star clusters dynamical evolution, with particular attention to the kinematical properties of the equilibrium configurations emerging at the end of this phase.We show that star clusters undergoing the process of violent relaxation in the tidal field of their host galaxy can acquire significant internal differential rotation and are characterized by a distinctive radial variation of the velocity anisotropy. These kinematical properties are the result of the symmetry breaking introduced by the external tidal field in the collapse phase and of the action of the Coriolis force on the orbit of the stars. The resulting equilibrium configurations are characterized by differential rotation, with a peak located between one and two half-mass radii. As for the anisotropy, similar to clusters evolving in isolation, the systems explored in this Letter are characterized by an inner isotropic core, followed by a region of increasing radial anisotropy. However for systems evolving in an external tidal field the degree of radial anisotropy reaches a maximum in the cluster intermediate regions and then progressively decreases, with the cluster outermost regions being characterized by isotropy or a mild tangential anisotropy. Young or old but less-relaxed dynamically young star clusters may keep memory of these kinematical fingerprints of their early dynamical evolution.Comment: 5 pages 4 figures. Accepted for publication in MNRAS Letter

Evolution of star clusters in a cosmological tidal field

We present a method to couple N-body star cluster simulations to a cosmological tidal field, using the Astrophysical Multipurpose Software Environment. We apply this method to star clusters embedded in the CosmoGrid dark matter-only LambdaCDM simulation. Our star clusters are born at z = 10 (corresponding to an age of the Universe of about 500 Myr) by selecting a dark matter particle and initializing a star cluster with 32,000 stars on its location. We then follow the dynamical evolution of the star cluster within the cosmological environment. We compare the evolution of star clusters in two Milky-Way size haloes with a different accretion history. The mass loss of the star clusters is continuous irrespective of the tidal history of the host halo, but major merger events tend to increase the rate of mass loss. From the selected two dark matter haloes, the halo that experienced the larger number of mergers tends to drive a smaller mass loss rate from the embedded star clusters, even though the final masses of both haloes are similar. We identify two families of star clusters: native clusters, which become part of the main halo before its final major merger event, and the immigrant clusters, which are accreted upon or after this event; native clusters tend to evaporate more quickly than immigrant clusters. Accounting for the evolution of the dark matter halo causes immigrant star clusters to retain more mass than when the z=0 tidal field is taken as a static potential. The reason for this is the weaker tidal field experienced by immigrant star clusters before merging with the larger dark matter halo.Comment: 14 pages, 14 figures, accepted for publication in MNRA

Analysis of global and regional CO burdens measured from space between 2000 and 2009 and validated by ground-based solar tracking spectrometers

Interannual variations in AIRS and MOPITT retrieved CO burdens are validated, corrected, and compared with CO emissions from wild fires from the Global Fire Emission Dataset (GFED2) inventory. Validation of daily mean CO total column (TC) retrievals from MOPITT version 3 and AIRS version 5 is performed through comparisons with archived TC data from the Network for Detection of Atmospheric Composition Change (NDACC) ground-based Fourier Transform Spectrometers (FTS) between March 2000 and December 2007. MOPITT V3 retrievals exhibit an increasing temporal bias with a rate of 1.4–1.8% per year; thus far, AIRS retrievals appear to be more stable. For the lowest CO values in the Southern Hemisphere (SH), AIRS TC retrievals overestimate FTS TC by 20%. MOPITT's bias and standard deviation do not depend on CO TC absolute values. Empirical corrections are derived for AIRS and MOPITT retrievals based on the observed annually averaged bias versus the FTS TC. Recently published MOPITT V4 is found to be in a good agreement with MOPITT V3 corrected by us (with exception of 2000–2001 period). With these corrections, CO burdens from AIRS V5 and MOPITT V3 (as well as MOPITT V4) come into good agreement in the mid-latitudes of the Northern Hemisphere (NH) and in the tropical belt. In the SH, agreement between AIRS and MOPITT CO burdens is better for the larger CO TC in austral winter and worse in austral summer when CO TC are smaller. Before July 2008, all variations in retrieved CO burden can be explained by changes in fire emissions. After July 2008, global and tropical CO burdens decreased until October before recovering by the beginning of 2009. The NH CO burden also decreased but reached a minimum in January 2009 before starting to recover. The decrease in tropical CO burdens is explained by lower than usual fire emissions in South America and Indonesia. This decrease in tropical emissions also accounts for most of the change in the global CO burden. However, no such diminution of NH biomass burning is indicated by GFED2. Thus, the CO burden decrease in the NH could result from a combination of lower fossil fuel emissions during the global economic recession and transport of CO-poor air from the tropics. More extensive modeling will be required to fully resolve this issue

The Gap Function Phi(k,w) for a Two-leg t-J Ladder and the Pairing Interaction

The gap function phi(k,omega), determined from a Lanczos calculation for a doped 2-leg t-J ladder, is used to provide insight into the spatial and temporal structure of the pairing interaction. It implies that this interaction is a local near-neighbor coupling which is retarded. The onset frequency of the interaction is set by the energy of an S=1 magnon-hole-pair and it is spread out over a frequency region of order the bandwith