Instruction: what is the prompt that generates the input?

Input: We investigate the possibility of a dark energy universe emerging from anaction with higher-order string loop corrections to Einstein gravity in thepresence of a massless dilaton. These curvature corrections (up to $R^4$ order)are different depending upon the type of (super)string model which isconsidered. We find in fact that Type II, heterotic, and bosonic stringsrespond differently to dark energy. A dark energy solution is shown to exist inthe case of the bosonic string, while the other two theories do not lead torealistic dark energy universes. Detailed analysis of the dynamical stabilityof the de-Sitter solution is presented for the case of a bosonic string. Ageneral prescription for the construction of a de-Sitter solution for thelow-energy (super)string effective action is also indicated. Beyond thelow-energy (super)string effective action, when the higher-curvature correctioncoefficients depend on the dilaton, the reconstruction of the theory from theuniverse expansion history is done with a corresponding prescription for thescalar potentials.


Instruction: what is the prompt that generates the input?

Input: To improve the quality of life in a modern society it is essential to reducethe distance between basic research and applications, whose crucial roles inshaping today's society prompt us to seek their understanding. Existing studieson this subject, however, have neglected the network character of theinteraction between university and industry. Here we use state-of-the-artnetwork theory methods to analyze this interplay in the so-called FrameworkProgramme--an initiative which sets out the priorities for the European Union'sresearch and technological development. In particular we study in the 5thFramework Programme (FP5) the role played by companies and scientificinstitutions and how they contribute to enhance the relationship betweenresearch and industry. Our approach provides quantitative evidence that whilefirms are size hierarchically organized, universities and researchorganizations keep the network from falling into pieces, paving the way for aneffective knowledge transfer.


Instruction: what is the prompt that generates the input?

Input: It is known that a subset of fractional quantum Hall wave functions has beenexpressed as conformal field theory (CFT) correlators, notably the Laughlinwave function at filling factor $\nu=1/m$ ($m$ odd) and its quasiholes, and thePfaffian wave function at $\nu=1/2$ and its quasiholes. We develop a generalscheme for constructing composite-fermion (CF) wave functions from conformalfield theory. Quasiparticles at $\nu=1/m$ are created by inserting anyonicvertex operators, $P_{\frac{1}{m}}(z)$, that replace a subset of the electronoperators in the correlator. The one-quasiparticle wave function is identicalto the corresponding CF wave function, and the two-quasiparticle wave functionhas correct fractional charge and statistics and is numerically almostidentical to the corresponding CF wave function. We further show how to exactlyrepresent the CF wavefunctions in the Jain series $\nu = s/(2sp+1)$ as the CFTcorrelators of a new type of fermionic vertex operators, $V_{p,n}(z)$,constructed from $n$ free compactified bosons; these operators provide the CFTrepresentation of composite fermions carrying $2p$ flux quanta in the $n^{\rmth}$ CF Landau level. We also construct the corresponding quasiparticle- andquasihole operators and argue that they have the expected fractional charge andstatistics. For filling fractions 2/5 and 3/7 we show that the chiral CFTs thatdescribe the bulk wave functions are identical to those given by Wen's generalclassification of quantum Hall states in terms of $K$-matrices and $l$- and$t$-vectors, and we propose that to be generally true. Our results suggest ageneral procedure for constructing quasiparticle wave functions for otherfractional Hall states, as well as for constructing ground states at fillingfractions not contained in the principal Jain series.


Instruction: what is the prompt that generates the input?

Input: We present a theoretical study of the density of states and supercurrent indiffusive superconductor-normal metal-superconductor (SNS) junctions. Inparticular, we study the influence on these two equilibrium properties of bothan arbitrary transparency of the SN interfaces and the presence of spin-flipscattering in the normal wire. We show that the minigap that is present in thespectrum of the diffusive wire is very sensitive to the interface transmission.More mportantly, we show that at arbitrary transparency the minigap replacesthe Thouless energy as the relevant energy scale for the proximity effect,determining for instance the temperature dependence of the critical current. Wealso study in detail how the critical current is suppressed by the effect ofspin-flip scattering, which can be due to either magnetic impurities or, undercertain circumstances, to an external magnetic field. Our analysis based on thequasiclassical theory of diffusive superconductors can be very valuable toestablish quantitative comparisons between experiment and theory.


Instruction: what is the prompt that generates the input?

Input: Phonon transmission across epitaxial interfaces is studied within the latticedynamic approach. The transmission shows weak dependence on frequency for thelattice wave with a fixed angle of incidence. The dependence on azimuth angleis found to be related to the symmetry of the boundary interface. Thetransmission varies smoothly with the change of the incident angle. A criticalangle of incidence exists when the phonon is incident from the side with largegroup velocities to the side with low ones. No significant mode conversion isobserved among different acoustic wave branches at the interface, except whenthe incident angle is near the critical value. Our theoretical result of theKapitza conductance $G_{K}$ across the Si-Ge (100) interface at temperature$T=200 $K is $4.6\times10^{8} {\rm WK}^{-1}{\rmm}^{-2}$. A scaling law $G_K\propto T^{2.87}$ at low temperature is also reported. Based on the features oftransmission obtained within lattice dynamic approach, we propose a simplifiedformula for thermal conductanceacross the epitaxial interface. A reasonableconsistency is found between the calculated values and the experimentallymeasured ones.


Instruction: what is the prompt that generates the input?

Input: We present a new, deep (V ~ 26) study of the Galactic globular cluster NGC2419 based on B,V,I time-series CCD photometry over about 10 years andextending beyond the cluster published tidal radius. We have identified 101variable stars of which 60 are new discoveries, doubling the known RR Lyraestars and including 12 SX Phoenicis stars. The average period of the RR Lyraestars (<Pab>=0.662 d, and <Pc>=0.366 d, for fundamental-mode -RRab- andfirst-overtone pulsators, respectively), and the position in theperiod-amplitude diagram both confirm that NGC 2419 is an Oosterhoff IIcluster. The average apparent magnitude of the RR Lyrae stars is <V>=20.31 +/-0.01 (sigma=0.06, 67 stars) and leads to the distance modulus (m-M)o=19.60 +/-0.05. The Color-Magnitude Diagram, reaching about 2.6 mag below the clusterturn-off, does not show clear evidence of multiple stellar populations. Clusterstars are found until r~ 10.5', and possibly as far as r~15', suggesting thatthe literature tidal radius might be underestimated. No extra-tidal structuresare clearly detected in the data. NGC 2419 has many blue stragglers and a wellpopulated horizontal branch extending from the RR Lyrae stars down to anextremely blue tail ending with the "blue-hook", for the first time recognizedin this cluster. The red giant branch is narrow ruling out significantmetallicity spreads. Our results seem to disfavor the interpretation of NGC2419 as either having an extragalactic origin or being the relict of a dwarfgalaxy tidally disrupted by the Milky Way.


Instruction: what is the prompt that generates the input?

Input: From photometric observations of elliptical galaxies, among which are bothradio galaxies and radio-quiet objects, an investigation was carried out of therelationship `redshift -- age of the stellar system' $(\Delta z/\Delta t)$. Bymeans of this relationship cosmological parameters $H(z)$ and $\Omega_\Lambda$are estimated. Ages of stellar systems are determined within the framework ofevolution models of synthetic spectra PEGASE and GISSEL. This approach can beconsidered as time study of objects of the early Universe independent of othercosmological models. Construction of a pooled sample is described, containing220 objects from different populations of elliptical galaxies, for which ananalysis of the upper limit of the age of formation of a stellar system wasperformed. These data were used to estimate the boundaries of determination ofthe cosmological parameters $H_0$ and $\Lambda$--term: $H_0=72\pm10$ and$\Omega_\Lambda=0.8\pm0.1$ in the model GISSEL and $H_0=53\pm10$, and$\Omega_\Lambda=0.8\pm0.1$ in the model PEGASE.


Instruction: what is the prompt that generates the input?

Input: Recent galaxy redshift surveys have brought in a large amount of accuratecosmological data out to redshift 0.3, and future surveys are expected toachieve a high degree of completeness out to a redshift exceeding 1.Consequently, a numerical programme for determining the metric of the universefrom observational data will soon become practical; and thereby realise theultimate application of Einstein's equations. Apart from detailing the cosmicgeometry, this would allow us to verify and quantify homogeneity, rather thanassuming it, as has been necessary up to now, and to do that on a metric level,and not merely at the mass distribution level. This paper is the beginning of aproject aimed at such a numerical implementation. The primary observationaldata from our past light cone consists of galaxy redshifts, apparentluminosities, angular diameters and number densities, together with sourceevolution functions, absolute luminosities, true diameters and masses ofsources. Here we start with the simplest case, that of spherical symmetry and adust equation of state, and execute an algorithm that determines the unknownmetric functions from this data. We discuss the challenges of turning thetheoretical algorithm into a workable numerical procedure, particularlyaddressing the origin and the maximum in the area distance. Our numericalmethod is tested with several artificial data sets for homogeneous andinhomogeneous models, successfully reproducing the original models. Thisdemonstrates the basic viability of such a scheme. Although current surveysdon't have sufficient completeness or accuracy, we expect this situation tochange in the near future, and in the meantime there are many refinements andgeneralisations to be added.


Instruction: what is the prompt that generates the input?

Input: We study the electron spin relaxation in intrinsic and $p$-type (001) GaAsquantum wells by constructing and numerically solving the kinetic spin Blochequations. All the relevant scatterings are explicitly included, especially thespin-flip electron-heavy hole exchange scattering which leads to theBir-Aronov-Pikus spin relaxation. We show that, due to the neglection of thenonlinear terms in the electron-heavy hole exchange scattering in theFermi-golden-rule approach, the spin relaxation due to the Bir-Aronov-Pikusmechanism is greatly exaggerated at moderately high electron density and lowtemperature in the literature. We compare the spin relaxation time due to theBir-Aronov-Pikus mechanism with that due to the D'yakonov-Perel' mechanismwhich is also calculated from the kinetic spin Bloch equations with all thescatterings, especially the spin-conserving electron-electron andelectron-heavy hole scatterings, included. We find that, in intrinsic quantumwells, the effect from the Bir-Aronov-Pikus mechanism is much smaller than thatfrom the D'yakonov-Perel' mechanism at low temperature, and it is smaller by nomore than one order of magnitude at high temperature. In $p$-type quantumwells, the spin relaxation due to the Bir-Aronov-Pikus mechanism is also muchsmaller than the one due to the D'yakonov-Perel' mechanism at low temperatureand becomes comparable to each other at higher temperature when the holedensity and the width of the quantum well are large enough. We claim thatunlike in the bulk samples, the Bir-Aronov-Pikus mechanism hardly dominates thespin relaxation in two-dimensional samples.


Instruction: what is the prompt that generates the input?

Input: We propose that genetic encoding of self-assembling components greatlyenhances the evolution of complex systems and provides an efficient platformfor inductive generalization, i.e. the inductive derivation of a solution to aproblem with a potentially infinite number of instances from a limited set oftest examples. We exemplify this in simulations by evolving scalable circuitryfor several problems. One of them, digital multiplication, has been intensivelystudied in recent years, where hitherto the evolutionary design of onlyspecific small multipliers was achieved. The fact that this and other problemscan be solved in full generality employing self-assembly sheds light on theevolutionary role of self-assembly in biology and is of relevance for thedesign of complex systems in nano- and bionanotechnology.


Instruction: what is the prompt that generates the input?

Input: Data mining is a useful decision support technique that can be used todiscover production rules in warehouses or corporate data. Data mining researchhas made much effort to apply various mining algorithms efficiently on largedatabases. However, a serious problem in their practical application is thelong processing time of such algorithms. Nowadays, one of the key challenges isto integrate data mining methods within the framework of traditional databasesystems. Indeed, such implementations can take advantage of the efficiencyprovided by SQL engines. In this paper, we propose an integrating approach fordecision trees within a classical database system. In other words, we try todiscover knowledge from relational databases, in the form of production rules,via a procedure embedding SQL queries. The obtained decision tree is defined bysuccessive, related relational views. Each view corresponds to a givenpopulation in the underlying decision tree. We selected the classical InductionDecision Tree (ID3) algorithm to build the decision tree. To prove that ourimplementation of ID3 works properly, we successfully compared the output ofour procedure with the output of an existing and validated data miningsoftware, SIPINA. Furthermore, since our approach is tuneable, it can begeneralized to any other similar decision tree-based method.


Instruction: what is the prompt that generates the input?

Input: We study the potential of the CNGS beam in constraining the parameter spaceof a model with one sterile neutrino separated from three active ones by an$\mathcal{O}(\eVq)$ mass-squared difference, $\Dmq_\Sbl$. We perform ouranalysis using the OPERA detector as a reference (our analysis can be upgradedincluding a detailed simulation of the ICARUS detector). We point out that thechannel with the largest potential to constrain the sterile neutrino parameterspace at the CNGS beam is $\nu_\mu \to \nu_\tau$. The reason for that istwofold: first, the active-sterile mixing angle that governs this oscillationis the less constrained by present experiments; second, this is the signal forwhich both OPERA and ICARUS have been designed, and thus benefits from anextremely low background. In our analysis we also took into account $\nu_\mu\to \nu_e$ oscillations. We find that the CNGS potential to look for sterileneutrinos is limited with nominal intensity of the beam, but it issignificantly enhanced with a factor 2 to 10 increase in the neutrino flux.Data from both channels allow us, in this case, to constrain further thefour-neutrino model parameter space. Our results hold for any value of$\Dmq_\Sbl \gtrsim 0.1 \eVq$, \textit{i.e.} when oscillations driven by thismass-squared difference are averaged. We have also checked that the bound on$\theta_{13}$ that can be put at the CNGS is not affected by the possibleexistence of sterile neutrinos.


Instruction: what is the prompt that generates the input?

Input: Pinpointing the progenitors of long duration gamma-ray bursts (LGRBs) remainsan extremely important question, although it is now clear that at least afraction of LGRBs originate in the core collapse of massive stars in type Icsupernovae, the pathways to the production of these stars, and their initialmasses, remain uncertain. Rotation is thought to be vital in the creation ofLGRBs, and it is likely that black hole creation is also necessary. We suggestthat these two constraints can be met if the GRB progenitors are very massivestars (>20 solar masses) and are formed in tight binary systems. Using simplemodels we compare the predictions of this scenario with observations and findthat the location of GRBs on their host galaxies are suggestive ofmain-sequence masses in excess of 20 solar masses, while 50% of the knowncompact binary systems may have been sufficiently close to have had thenecessary rotation rates for GRB creation. Thus, massive stars in compactbinaries are a likely channel for at least some fraction of LGRBs.


Instruction: what is the prompt that generates the input?

Input: Prices of commodities or assets produce what is called time-series. Differentkinds of financial time-series have been recorded and studied for decades.Nowadays, all transactions on a financial market are recorded, leading to ahuge amount of data available, either for free in the Internet or commercially.Financial time-series analysis is of great interest to practitioners as well asto theoreticians, for making inferences and predictions. Furthermore, thestochastic uncertainties inherent in financial time-series and the theoryneeded to deal with them make the subject especially interesting not only toeconomists, but also to statisticians and physicists. While it would be aformidable task to make an exhaustive review on the topic, with this review wetry to give a flavor of some of its aspects.


Instruction: what is the prompt that generates the input?

Input: Electrons in solids have been conventionally classified as either band-likeitinerant ones or atomic-like localized ones depending on their properties. Forheavy Fermion (HF) compounds, however, the f electrons show both itinerant andlocalized behaviours depending on temperature. Above the characteristictemperature T*, which is typically of the order of few K to few tens K, theirmagnetic properties are well described by the ionic f-electron models,suggesting that the f-electrons behave as 'localized' electrons. On the otherhand, well below T*, their Fermi surfaces (FS's) have been observed bymagneto-oscillatory techniques, and generally they can be explained well by the'itinerant' f-electron model. These two models assume totally different naturesof felectrons, and how they transform between localized and itinerant state asa function of temperatures has never been understood on the level of theirelectronic structures. Here we have studied the band structure of the HFantiferromagnetic superconductor UPd2Al3 well below and above T* byangle-resolved photoelectron spectroscopy (ARPES), and revealed the temperaturedependence of the electronic structure. We have found that the f-bands, whichform the FS's at low temperatures are excluded from FS's at high temperatures.The present results demonstrate how the same f-electrons show both itinerantand localized behaviours on the level of electronic structure, and provide animportant information for the unified description of the localized anditinerant nature of HF compounds.


Instruction: what is the prompt that generates the input?

Input: If the binding energy of the pulsar's surface is not so high (the case of aneutron star), both the negative and positive charges will flow out freely fromthe surface of the star. The annular free flow model for $\gamma$-ray emissionof pulsars is suggested in this paper. It is emphasized that: (1). Two kinds ofacceleration regions (annular and core) need to be taken into account. Theannular acceleration region is defined by the magnetic field lines that crossthe null charge surface within the light cylinder. (2). If the potential dropin the annular region of a pulsar is high enough (normally the cases of youngpulsars), charges in both the annular and the core regions could be acceleratedand produce primary gamma-rays. Secondary pairs are generated in both regionsand stream outwards to power the broadband radiations. (3). The potential dropin the annular region grows more rapidly than that in the core region. Theannular acceleration process is a key point to produce wide emission beams asobserved. (4). The advantages of both the polar cap and outer gap models areretained in this model. The geometric properties of the $\gamma$-ray emissionfrom the annular flow is analogous to that presented in a previous work by Qiaoet al., which match the observations well. (5). Since charges with differentsigns leave the pulsar through the annular and the core regions, respectively,the current closure problem can be partially solved.


Instruction: what is the prompt that generates the input?

Input: The two-body interaction in dilute solutions of polymer chains in goodsolvents can be modeled by means of effective bounded potentials, the simplestof which being that of penetrable spheres (PSs). In this paper we construct twosimple analytical theories for the structural properties of PS fluids: alow-temperature (LT) approximation, that can be seen as an extension to PSs ofthe well-known solution of the Percus-Yevick (PY) equation for hard spheres,and a high-temperature (HT) approximation based on the exact asymptoticbehavior in the limit of infinite temperature. Monte Carlo simulations for awide range of temperatures and densities are performed to assess the validityof both theories. It is found that, despite their simplicity, the HT and LTapproximations exhibit a fair agreement with the simulation data within theirrespective domains of applicability, so that they complement each other. Acomparison with numerical solutions of the PY and the hypernetted-chainapproximations is also carried out, the latter showing a very good performance,except inside the core at low temperatures.


Instruction: what is the prompt that generates the input?

Input: The aim of the KArlsruhe TRItium Neutrino experiment KATRIN is thedetermination of the absolute neutrino mass scale down to 0.2 eV, withessentially smaller model dependence than from cosmology and neutrinolessdouble beta decay. For this purpose, the integral electron energy spectrum ismeasured close to the endpoint of molecular tritium beta decay. The endpoint,together with the neutrino mass, should be fitted from the KATRIN data as afree parameter. The right-handed couplings change the electron energy spectrumclose to the endpoint, therefore they have some effect also to the preciseneutrino mass determination. The statistical calculations show that, using theendpoint as a free parameter, the unaccounted right-handed couplingsconstrained by many beta decay experiments can change the fitted neutrino massvalue, relative to the true neutrino mass, by not larger than about 5-10 %.Using, incorrectly, the endpoint as a fixed input parameter, the above changeof the neutrino mass can be much larger, order of 100 %, and for some cases itcan happen that for large true neutrino mass value the fitted neutrino masssquared is negative. Publications using fixed endpoint and presenting largeright-handed coupling effects to the neutrino mass determination are notrelevant for the KATRIN experiment.


Instruction: what is the prompt that generates the input?

Input: The development and progress of the studies of winds and mass loss from hotstars, from about 1965 up to now, is discussed in a personal historicalperspective. The present state of knowledge about stellar winds, based onpapers presented at this workshop, is described. About ten years ago themechanisms of the winds were reasonably well understood, the mass loss rateswere known, and the predictions of stellar evolution theory with mass lossagreed with observations. However, recent studies especially those based onFUSE observations, have resulted in a significant reduction of the mass lossrates, that disagrees with predictions from radiation driven wind models. Thesituation is discussed and future studies that can clarify the situation aresuggested.  I also discuss what is known about the dissolution of star clusters indifferent environments. The dissolution time can be derived from the mass andage distributions of cluster samples. The resulting dissolution times ofclusters in the solar neighborhood (SN) and in interacting galaxies are shorterthan predicted by two-body relaxation of clusters in a tidal field. Encounterswith giant molecular clouds can explain the fate of clusters in the SN and arethe most likely cause of the short lifetime of clusters in interactinggalaxies.


Instruction: what is the prompt that generates the input?

Input: Aiming at a better understand of the physical and chemical processes in thehot molecular core stage of high-mass star formation, we observed theprototypical hot core G29.96-0.02 in the 862mu band with the SubmillimeterArray (SMA) at sub-arcsecond spatial resolution. The observations resolved thehot molecular core into six submm continuum sources with the finest spatialresolution of 0.36''x0.25'' (~1800AU) achieved so far. Four of them locatedwithin 7800(AU)^2 comprise a proto-Trapezium system with estimated protostellardensities of 1.4x0^5 protostars/pc^3. The plethora of ~80 spectral lines allowsus to study the molecular outflow(s), the core kinematics, the temperaturestructure of the region as well as chemical effects. The derived hot coretemperatures are of the order 300K. We find interesting chemical spatialdifferentiations, e.g., C34S is deficient toward the hot core and is enhancedat the UCHII/hot core interface, which may be explained by temperaturesensitive desorption from grains and following gas phase chemistry. TheSiO(8-7) emission outlines likely two molecular outflows emanating from thishot core region. Emission from most other molecules peaks centrally on the hotcore and is not dominated by any individual submm peak. Potential reasons forthat are discussed. A few spectral lines that are associated with the mainsubmm continuum source, show a velocity gradient perpendicular to thelarge-scale outflow. Since this velocity structure comprises three of thecentral protostellar sources, this is not a Keplerian disk. While the data areconsistent with a gas core that may rotate and/or collapse, we cannot excludethe outflow(s) and/or nearby expanding UCHII region as possible alternativecauses of this velocity pattern.


Instruction: what is the prompt that generates the input?

Input: In a data warehousing process, the data preparation phase is crucial.Mastering this phase allows substantial gains in terms of time and performancewhen performing a multidimensional analysis or using data mining algorithms.Furthermore, a data warehouse can require external data. The web is a prevalentdata source in this context, but the data broadcasted on this medium are veryheterogeneous. We propose in this paper a UML conceptual model for a complexobject representing a superclass of any useful data source (databases, plaintexts, HTML and XML documents, images, sounds, video clips...). The translationinto a logical model is achieved with XML, which helps integrating all thesediverse, heterogeneous data into a unified format, and whose schema definitionprovides first-rate metadata in our data warehousing context. Moreover, webenefit from XML's flexibility, extensibility and from the richness of thesemi-structured data model, but we are still able to later map XML documentsinto a database if more structuring is needed.


Instruction: what is the prompt that generates the input?

Input: This paper includes a reflection on the role of networks in the study ofEnglish language acquisition, as well as a collection of practical criteria toannotate free-speech corpora from children utterances. At the theoreticallevel, the main claim of this paper is that syntactic networks should beinterpreted as the outcome of the use of the syntactic machinery. Thus, theintrinsic features of such machinery are not accessible directly from (known)network properties. Rather, what one can see are the global patterns of its useand, thus, a global view of the power and organization of the underlyinggrammar. Taking a look into more practical issues, the paper examines how tobuild a net from the projection of syntactic relations. Recall that, as opposedto adult grammars, early-child language has not a well-defined concept ofstructure. To overcome such difficulty, we develop a set of systematic criteriaassuming constituency hierarchy and a grammar based on lexico-thematicrelations. At the end, what we obtain is a well defined corpora annotation thatenables us i) to perform statistics on the size of structures and ii) to builda network from syntactic relations over which we can perform the standardmeasures of complexity. We also provide a detailed example.


Instruction: what is the prompt that generates the input?

Input: The main result of this article is the fact that the currents defined byLevin give a description of the polylogarithm of an abelian scheme at thetopological level. This result was a conjecture of Levin. This provides amethod to explicit the Eisenstein classes of an abelian scheme at thetopological level. These classes are of special interest since they have amotivic origin by a theorem of Kings. In a forthcoming article, we use the mainresult of this paper to prove that the Eisenstein classes of the universalabelian scheme over an Hilbert-Blumenthal variety degenerate at the boundary ofthe Baily-Borel compactification of the base in a special value of an$L$-function associated to the underlying totally real number field. As acorollary, we get a non vanishing result for some of these Eisenstein classesin this geometric situation.


Instruction: what is the prompt that generates the input?

Input: We investigate the use of optical variability to identify and study ActiveGalactic Nuclei (AGN) in the GOODS-South field. A sample of 22 mid-infraredpower law sources and 102 X-ray sources with optical counterparts in the HSTACS images were selected. Each object is classified with a variabilitysignificance value related to the standard deviation of its magnitude in fiveepochs separated by 45-day intervals. The variability significance is comparedto the optical, mid-IR, and X-ray properties of the sources. We find that 26%of all AGN candidates (either X-ray- or mid-IR-selected) are optical variables.The fraction of optical variables increases to 51% when considering sourceswith soft X-ray band ratios. For the mid-IR AGN candidates which havemultiwavelength SEDs, we find optical variability for 64% of those classifiedwith SEDs like Broad Line AGNs. While mostly unobscured AGN appear to have themost significant optical variability, some of the more obscured AGNs are alsoobserved as variables. In particular, we find two mid-IR power law-selected AGNcandidates without X-ray emission that display optical variability, confirmingtheir AGN nature.


Instruction: what is the prompt that generates the input?

Input: In this paper we consider magnetic Schr\"odinger operators in R^n, n \ge 3.Under almost optimal conditions on the potentials in terms of decay andregularity we prove smoothing and Strichartz estimates, as well as a limitingabsorption principle. For large gradient perturbations the latter is not acorollary of the free case as the differentiated free resolvent does not havesmall operator norm on any weighted L^2 spaces.  We instead show that the spectral radius of such operators decreases to zero,hence their perturbation of the identity is still invertible. The key estimatesare based on an angular decomposition of the free resolvent, or rather a boundthat holds uniformly for all possible angular decompositions. The proof avoidsthe Fourier transform and instead uses H\"ormander's variable coefficientPlancherel theorem for oscillatory integrals.


Instruction: what is the prompt that generates the input?

Input: We constrain blastwave parameters and the circumburst media of a subsample often BeppoSAX Gamma-Ray Bursts. For this sample we derive the values of theinjected electron energy distribution index, p, and the density structure indexof the circumburst medium, k, from simultaneous spectral fits to their X-ray,optical and nIR afterglow data. The spectral fits have been done in count spaceand include the effects of metallicity, and are compared with the previouslyreported optical and X-ray temporal behaviour. Using the blastwave model andsome assumptions which include on-axis viewing and standard jet structure,constant blastwave energy and no evolution of the microphysical parameters, wefind a mean value of p for the sample as a whole of 2.04 +0.02/-0.03. Astatistical analysis of the distribution demonstrates that the p values in thissample are inconsistent with a single universal value for p at the 3-sigmalevel or greater, which has significant implications for particle accelerationmodels. This approach provides us with a measured distribution of circumburstdensity structures rather than considering only the cases of k=0 (homogeneous)and k=2 (wind-like). We find five GRBs for which k can be well constrained, andin four of these cases the circumburst medium is clearly wind-like. The fifthsource has a value of 0<k<1, consistent with a homogeneous circumburst medium.


Instruction: what is the prompt that generates the input?

Input: In this work we compare and characterize the behavior of Langevin andDissipative Particle Dynamics (DPD) thermostats in a broad range ofnon-equilibrium simulations of polymeric systems. Polymer brushes in relativesliding motion, polymeric liquids in Poiseuille and Couette flows, andbrush-melt interfaces are used as model systems to analyze the efficiency andlimitations of different Langevin and DPD thermostat implementations. Widelyused coarse-grained bead-spring models under good and poor solvent conditionsare employed to assess the effects of the thermostats. We consideredequilibrium, transient, and steady state examples for testing the ability ofthe thermostats to maintain constant temperature and to reproduce theunderlying physical phenomena in non-equilibrium situations. The commonpractice of switching-off the Langevin thermostat in the flow direction is alsocritically revisited. The efficiency of different weight functions for the DPDthermostat is quantitatively analyzed as a function of the solvent quality andthe non-equilibrium situation.


Instruction: what is the prompt that generates the input?

Input: We report discovery of a compact object at high Galactic latitude. The objectwas initially identified as a ROSAT All-Sky Survey Bright Source Catalog X-raysource, 1RXS J141256.0+792204, statistically likely to possess a high X-ray tooptical flux ratio. Further observations using {\em  Swift}, Gemini-North, and the Chandra X-ray Observatory refined the sourceposition and confirmed the absence of any optical counterpart to an X-ray tooptical flux ratio of F_X/F_V > 8700 (3 sigma). Interpretation of 1RXSJ141256.0+792204 -- which we have dubbed Calvera -- as a typical X-ray-dimisolated neutron star would place it at z ~ 5.1 kpc above the Galactic disk --in the Galactic halo -- implying that it either has an extreme space velocity(v_z >~ 5100 km s-1) or has failed to cool according to theoreticalpredictions. Interpretations as a persistent anomalous X-ray pulsar, or a``compact central object'' present conflicts with these classes' typicalproperties. We conclude the properties of Calvera are most consistent withthose of a nearby (80 to 260 pc) radio pulsar, similar to the radio millisecondpulsars of 47 Tuc, with further observations required to confirm thisclassification. If it is a millisecond pulsar, it has an X-ray flux equal tothe X-ray brightest millisecond pulsar (and so is tied for highest flux); isthe closest northern hemisphere millisecond pulsar; and is potentially theclosest known millisecond pulsar in the sky, making it an interesting targetfor X-ray-study, a radio pulsar timing array, and LIGO.


Instruction: what is the prompt that generates the input?

Input: All possible transformations from the Robertson-Walker metric to thoseconformal to the Lorentz-Minkowski form are derived. It is demonstrated thatthe commonly known family of transformations and associated conformal factorsare not exhaustive and that there exists another relatively less well knownfamily of transformations with a different conformal factor in the particularcase that K = -1. Simplified conformal factors are derived for the special caseof maximally-symmetric spacetimes. The full set of all possiblecosmologically-compatible conformal forms is presented as a comprehensivetable. A product of the analysis is the determination of the set-theoreticalrelationships between the maximally symmetric spacetimes, the Robertson-Walkerspacetimes, and functionally more general spacetimes. The analysis is precededby a short historical review of the application of conformal metrics toCosmology.


Instruction: what is the prompt that generates the input?

Input: We present the discovery of two very-high-energy gamma-ray sources in anongoing systematic search for emission above 100 GeV from pulsar wind nebulaein survey data from the H.E.S.S. telescope array. Imaging Atmospheric CherenkovTelescopes are ideal tools for searching for extended emission from pulsar windnebulae in the very-high-energy regime. H.E.S.S., with its large field of viewof 5 degrees and high sensitivity, gives new prospects for the search for theseobjects. An ongoing systematic search for very-high-energy emission fromenergetic pulsars over the region of the Galactic plane between -60 degrees < l< 30 degrees, -2 degrees < b < 2 degrees is performed. For the resultingcandidates, the standard H.E.S.S. analysis was applied and a search formulti-wavelength counterparts was performed. We present the discovery of twonew candidate gamma-ray pulsar wind nebulae, HESS J1718-385 and HESS J1809-193.H.E.S.S. has proven to be a suitable instrument for pulsar wind nebulasearches.


Instruction: what is the prompt that generates the input?

Input: An easily implementable path solution algorithm for 2D spatial problems,based on excitable/programmable characteristics of a specific cellularnonlinear network (CNN) model is presented and numerically investigated. Thenetwork is a single layer bioinspired model which was also implemented in CMOStechnology. It exhibits excitable characteristics with regionally bistablecells. The related response realizes propagations of trigger autowaves, wherethe excitable mode can be globally preset and reset. It is shown that, obstacledistributions in 2D space can also be directly mapped onto the coupled cellarray in the network. Combining these two features, the network model can serveas the main block in a 2D path computing processor. The related algorithm andconfigurations are numerically experimented with circuit level parameters andperformance estimations are also presented. The simplicity of the model alsoallows alternative technology and device level implementation, which may becomecritical in autonomous processor design of related micro or nanoscale roboticapplications.


Instruction: what is the prompt that generates the input?

Input: This paper is the continuation of a previous one [L. {\v{S}}amaj and B.Jancovici, 2007 {\it J. Stat. Mech.} P02002]; for a nearly classical quantumfluid in a half-space bounded by a plain plane hard wall (no image forces), wehad generalized the Wigner-Kirkwood expansion of the equilibrium statisticalquantities in powers of Planck's constant $\hbar$. As a model system for a moredetailed study, we consider the quantum two-dimensional one-component plasma: asystem of charged particles of one species, interacting through the logarithmicCoulomb potential in two dimensions, in a uniformly charged background ofopposite sign, such that the total charge vanishes. The corresponding classicalsystem is exactly solvable in a variety of geometries, including the presentone of a half-plane, when $\beta e^2=2$, where $\beta$ is the inversetemperature and $e$ is the charge of a particle: all the classical $n$-bodydensities are known. For the quantum one-component plasma, two sum rulesinvolving the truncated two-body density (and, for one of them, the densityprofile) have been derived, a long time ago, by heuristic macroscopicarguments: one sum rule is about the asymptotic form along the wall of thetruncated two-body density, the other one is about the dipole moment of thestructure factor. In the two-dimensional case at $\beta e^2=2$, we have nowexplicit expressions up to order $\hbar^2$ of these two quantum densities, thuswe can microscopically check the sum rules at this order. The checks arepositive, reinforcing the idea that the sum rules are correct.


Instruction: what is the prompt that generates the input?

Input: We present a scaling law that predicts the values of the stresses obtained innumerical simulations of saturated MRI-driven turbulence in non-stratifiedshearing boxes. It relates the turbulent stresses to the strength of thevertical magnetic field, the sound speed, the vertical size of the box, and thenumerical resolution and predicts accurately the results of 35 numericalsimulations performed for a wide variety of physical conditions. We use ourresult to show that the saturated stresses in simulations with zero netmagnetic flux depend linearly on the numerical resolution and would becomenegligible if the resolution were set equal to the natural dissipation scale inastrophysical disks. We conclude that, in order for MRI-driven turbulentangular momentum transport to be able to account for the large value of theeffective alpha viscosity inferred observationally, the disk must be threadedby a significant vertical magnetic field and the turbulent magnetic energy mustbe in near equipartition with the thermal energy. This result has importantimplications for the spectra of accretion disks and their stability.


Instruction: what is the prompt that generates the input?

Input: We present the latest catalog of more than 1200 spectroscopically-selectedclose binary systems observed with the Sloan Digital Sky Survey through DataRelease Five. We use the catalog to search for magnetic white dwarfs incataclysmic variable progenitor systems. Given that approximately 25% ofcataclysmic variables contain a magnetic white dwarf, and that our large sampleof close binary systems should contain many progenitors of cataclysmicvariables, it is quite surprising that we find only two potential magneticwhite dwarfs in this sample. The candidate magnetic white dwarfs, if confirmed,would possess relatively low magnetic field strengths (B_WD < 10 MG) that aresimilar to those of intermediate-Polars but are much less than the averagefield strength of the current Polar population. Additional observations ofthese systems are required to definitively cast the white dwarfs as magnetic.Even if these two systems prove to be the first evidence of detached magneticwhite dwarf + M dwarf binaries, there is still a large disparity between theproperties of the presently known cataclysmic variable population and thepresumed close binary progenitors.


Instruction: what is the prompt that generates the input?

Input: An extensive set of optical and NIR photometry and low-resolution spectra theType Ia supernova (SN Ia) 2003du was obtained using a number of facilities. Theobservations started 13 days before B-band maximum light and continued for 480days with exceptionally good time sampling. The optical photometry wascalibrated through the S-correction technique.  The UBVRIJHK light curves and the color indices of SN 2003du closely resemblethose of normal SNe Ia. SN 2003du reached a B-band maximum of 13.49 (+/-0.02)mag on JD2452766.38 (+/-0.5). We derive a B-band stretch parameter of 0.988(+/-0.003), which corresponds to dM15=1.02 (+/-0.05), indicative of a SN Ia ofstandard luminosity. The reddening in the host galaxy was estimated by threemethods, and was consistently found to be negligible. We estimate a distancemodulus of 32.79 (+/-0.15) mag to the host galaxy, UGC 9391. The peak UVOIRbolometric luminosity of 1.35(+/-0.20) 10^43 erg/s and Arnett's rule impliesthat M(Ni56)=0.68 (+/-0.14)M_sun of Ni56 was synthesized during the explosion.Modeling of the UVOIR bolometric light curve also indicates M(Ni56) in therange 0.6-0.8 M_sun. The spectral evolution of SN 2003du at both optical andNIR wavelengths also closely resembles normal SNe Ia. In particular, the Si IIratio at maximum R(Si II)=0.22 (+/-0.02) and the time evolution of theblueshift velocities of the absorption line minima are typical. The pre-maximumspectra of SN 2003du showed conspicuous high-velocity features in the Ca II H&Kdoublet and infrared triplet, and possibly in Si II 6355, lines. We compare thetime evolution of the profiles of these lines with other well-observed SNe Iaand we suggest that the peculiar pre-maximum evolution of Si II 6355 line inmany SNe Ia is due to the presence of two blended absorption components.


Instruction: what is the prompt that generates the input?

Input: The extended Hubbard Hamiltonian is a widely accepted model for uncoveringthe effects of strong correlations on the phase diagram of low-dimensionalsystems, and a variety of theoretical techniques have been applied to it. Inthis paper the world-line quantum Monte Carlo method is used to study spin,charge, and bond order correlations of the one-dimensional extended Hubbardmodel in the presence of coupling to the lattice. A static alternating latticedistortion (the ionic Hubbard model) leads to enhanced charge density wavecorrelations at the expense of antiferromagnetic order. When the latticedegrees of freedom are dynamic (the Hubbard-Holstein model), we show that asimilar effect occurs even though the charge asymmetry must arisespontaneously. Although the evolution of the total energy with lattice couplingis smooth, the individual components exhibit sharp crossovers at the phaseboundaries. Finally, we observe a tendency for bond order in the region betweenthe charge and spin density wave phases.


Instruction: what is the prompt that generates the input?

Input: [Abridged] In galactic nuclei with sufficiently short relaxation times,binary supermassive black holes can evolve beyond their stalling radii viacontinued interaction with stars. We study this "collisional" evolutionaryregime using both fully self-consistent N-body integrations and approximateFokker-Planck models. The N-body integrations employ particle numbers up to0.26M and a direct-summation potential solver; close interactions involving thebinary are treated using a new implementation of the Mikkola-Aarseth chainregularization algorithm. Even at these large values of N, two-body scatteringoccurs at high enough rates in the simulations that they can not be simplyscaled to the large-N regime of real galaxies. The Fokker-Planck model is usedto bridge this gap; it includes, for the first time, binary-induced changes inthe stellar density and potential. The Fokker-Planck model is shown toaccurately reproduce the results of the N-body integrations, and is thenextended to the much larger N regime of real galaxies. Analytic expressions arederived that accurately reproduce the time dependence of the binary semi-majoraxis as predicted by the Fokker-Planck model. Gravitational wave coalescence isshown to occur in <10 Gyr in nuclei with velocity dispersions below about 80km/s. Formation of a core results from a competition between ejection of starsby the binary and re-supply of depleted orbits via two-body scattering. Massdeficits as large as ~4 times the binary mass are produced before coalescence.After the two black holes coalesce, a Bahcall-Wolf cusp appears around thesingle hole in one relaxation time, resulting in a nuclear density profileconsisting of a flat core with an inner, compact cluster, similar to what isobserved at the centers of low-luminosity spheroids.


Instruction: what is the prompt that generates the input?

Input: We present new multi-wavelength millimeter interferometric observations ofthe Herbig Ae star HD 163296 obtained with the IRAM/PBI, SMA and VLA arraysboth in continuum and in the 12CO, 13CO and C18O emission lines. Gas and dustproperties have been obtained comparing the observations with self-consistentdisk models for the dust and CO emission. The circumstellar disk is resolvedboth in the continuum and in CO. We find strong evidence that the circumstellarmaterial is in Keplerian rotation around a central star of 2.6 Msun. The diskinclination with respect to the line of sight is 46+-4 deg with a positionangle of 128+-4 deg. The slope of the dust opacity measured between 0.87 and 7mm (beta=1) confirms the presence of mm/cm-size grains in the disk midplane.The dust continuum emission is asymmetric and confined inside a radius of 200AU while the CO emission extends up to 540 AU. The comparison between dust andCO temperature indicates that CO is present only in the disk interior. Finally,we obtain an increasing depletion of CO isotopomers from 12CO to 13CO and C18O.We argue that these results support the idea that the disk of HD 163296 isstrongly evolved. In particular, we suggest that there is a strong depletion ofdust relative to gas outside 200 AU; this may be due to the inward migration oflarge bodies that form in the outer disk or to clearing of a large gap in thedust distribution by a low mass companion.


Instruction: what is the prompt that generates the input?

Input: We model energy dependencies of the quasi periodic oscillations (QPO) in themodel of disc epicyclic motions, with X-ray modulation caused by varyingrelativistic effects. The model was proposed to explain the high frequency QPOobserved in X-ray binaries. We consider two specific scenarios for the geometryof accretion flow and spectral formation. Firstly, a standard cold accretiondisc with an active X-ray emitting corona is assumed to oscillate. Secondly,only a hot X-ray emitting accretion flow oscillates, while the cold disc isabsent at the QPO radius. We find that the QPO spectra are generally similar tothe spectrum of radiation emitted at the QPO radius, and they are broadened bythe relativistic effects. In particular, the QPO spectrum contains the disccomponent in the oscillating disc with a corona scenario. We also review theavailable data on energy dependencies of high frequency QPO, and we point outthat they appear to lack the disc component in their energy spectra. This wouldsuggest the hot flow geometry in the spectral states when high frequency QPOare observed.


Instruction: what is the prompt that generates the input?

Input: A study of the $p d \to p d \eta$ reaction in the energy range where therecent data from Uppsala are available, is done in the two-step model of $\eta$production including the final state interaction. The $\eta -d$ final stateinteraction is incorporated through the solution of the Lippmann Schwingerequation using an elastic scattering matrix element, $T_{\eta d \to \eta d}$,which is required to be half off-shell. It is written in a factorized form,with an off-shell form factor multiplying an on-shell part given by aneffective range expansion up to the fourth power in momentum. The parameters ofthis expansion have been taken from an existing recent relativistic Faddeevequation solution for the $\eta NN$ system corresponding to different $\eta-N$scattering amplitudes. Calculations have also been done using few bodyequations within a finite rank approximation (FRA) to generate $T_{\eta d \to\eta d}$. The $p-d$ final state interaction is included in the spirit of theWatson-Migdal prescription by multiplying the matrix element by the inverse ofthe Jost function. The $\eta-d$ interaction is found to be dominant in theregion of small invariant $\eta -d$ mass, $M_{\eta d}$. The $p-d$ interactionenhances the cross section in the whole region of $M_{\eta d}$, but is largerfor large $M_{\eta d}$. We find nearly isotropic angular distributions of theproton and the deuteron in the final state. All the above observations are inagreement with data. The production mechanism for the entire range of theexisting data on the $p d \to p d \eta$ reaction seems to be dominated by thetwo-step model of $\eta$ production.


Instruction: what is the prompt that generates the input?

Input: We consider a class of real random polynomials, indexed by an integer d, oflarge degree n and focus on the number of real roots of such randompolynomials. The probability that such polynomials have no real root in theinterval [0,1] decays as a power law n^{-\theta(d)} where \theta(d)>0 is theexponent associated to the decay of the persistence probability for thediffusion equation with random initial conditions in space dimension d. For neven, the probability that such polynomials have no root on the full real axisdecays as n^{-2(\theta(d) + \theta(2))}. For d=1, this connection allows for aphysical realization of real random polynomials. We further show that theprobability that such polynomials have exactly k real roots in [0,1] has anunusual scaling form given by n^{-\tilde \phi(k/\log n)} where \tilde \phi(x)is a universal large deviation function.


Instruction: what is the prompt that generates the input?

Input: The luminosity and the spectral distribution of the afterglow of GRB 031203have been presented within our theoretical framework, which envisages the GRBstructure as composed by a proper-GRB, emitted at the transparency of anelectron-positron plasma with suitable baryon loading, and an afterglowcomprising the "prompt emission" as due to external shocks. In addition to theGRB emission, there appears to be a prolonged soft X-Ray emission lasting for10^6-10^7 seconds followed by an exponential decay. This additional source hasbeen called by us URCA-3. It is urgent to establish if this component isrelated to the GRB or to the Supernova (SN). In this second case, there are twopossibilities: either the interaction of the SN ejecta with the interstellarmedium or, possibly, the cooling of a young neutron star formed in the SN2003lw process. The analogies and the differences between this triptych GRB031203 / SN 2003lw / URCA-3 and the corresponding ones GRB 980425 / SN 1998bw /URCA-1 and GRB 030329 / SN 2003dh / URCA-2, as well as GRB 060218 / SN 2006ajare discussed.


Instruction: what is the prompt that generates the input?

Input: In scintillator detectors, the forward displacement of the neutron in thereaction $\bar\nu_e+p\to e^++n$ provides neutrino directional information asdemonstrated by the CHOOZ reactor experiment with 2,500 events. The neardetector of the forthcoming Double Chooz experiment will collect$1.6\times10^5$ events per year, enough to determine the average neutrinodirection with a $1 \sigma$ half-cone aperture of $2.3^\circ$ in one year. Itis more difficult to separate the two Chooz reactors that are viewed at aseparation angle $\phi=30^\circ$. If their strengths are known andapproximately equal, the azimuthal location of each reactor is obtained with$\pm6^\circ$ ($1 \sigma$) and the probability of confusing them with a singlesource is less than 11%. Five year's data reduce this ``confusion probability''to less than 0.3%, i.e., a $3 \sigma$ separation is possible. All of thesenumbers improve rapidly with increasing angular separation of the sources. Fora setup with $\phi=90^\circ$ and one year's data, the azimuthal $1 \sigma$uncertainty for each source decreases to $\pm3.2^\circ$. Of course, for DoubleChooz the two reactor locations are known, allowing one instead to measuretheir individual one-year integrated power output to $\pm11%$ ($1 \sigma$), andtheir five-year integrated output to $\pm4.8%$ ($1 \sigma$).


Instruction: what is the prompt that generates the input?

Input: We address the inverse problem of cosmic large-scale structure reconstructionfrom a Bayesian perspective. For a linear data model, a number of known andnovel reconstruction schemes, which differ in terms of the underlying signalprior, data likelihood, and numerical inverse extra-regularization schemes arederived and classified. The Bayesian methodology presented in this paper triesto unify and extend the following methods: Wiener-filtering, Tikhonovregularization, Ridge regression, Maximum Entropy, and inverse regularizationtechniques. The inverse techniques considered here are the asymptoticregularization, the Jacobi, Steepest Descent, Newton-Raphson,Landweber-Fridman, and both linear and non-linear Krylov methods based onFletcher-Reeves, Polak-Ribiere, and Hestenes-Stiefel Conjugate Gradients. Thestructures of the up-to-date highest-performing algorithms are presented, basedon an operator scheme, which permits one to exploit the power of fast Fouriertransforms. Using such an implementation of the generalized Wiener-filter inthe novel ARGO-software package, the different numerical schemes arebenchmarked with 1-, 2-, and 3-dimensional problems including structured whiteand Poissonian noise, data windowing and blurring effects. A novel numericalKrylov scheme is shown to be superior in terms of performance and fidelity.These fast inverse methods ultimately will enable the application of samplingtechniques to explore complex joint posterior distributions. We outline how thespace of the dark-matter density field, the peculiar velocity field, and thepower spectrum can jointly be investigated by a Gibbs-sampling process. Such amethod can be applied for the redshift distortions correction of the observedgalaxies and for time-reversal reconstructions of the initial density field.


Instruction: what is the prompt that generates the input?

Input: Inelastic and elastic neutron scattering is used to study spin correlationsin the quasi-one dimensional quantum antiferromagnet IPA-CuCl3 in strongapplied magnetic fields. A condensation of magnons and commensurate transverselong-range ordering is observe at a critical filed $H_c=9.5$ T. The fielddependencies of the energies and polarizations of all magnon branches areinvestigated both below and above the transition point. Their dispersion ismeasured across the entire 1D Brillouin zone in magnetic fields up to 14 T. Thecritical wave vector of magnon spectrum truncation [Masuda et al., Phys. Rev.Lett. 96, 047210 (2006)] is found to shift from h_c 0.35 at H>H_c. A drasticreduction of magnon bandwidths in the ordered phase [Garlea et al., Phys. Rev.Lett. 98, 167202 (2007)] is observed and studied in detail. New features of thespectrum, presumably related to this bandwidth collapse, are observed justabove the transition field.


Instruction: what is the prompt that generates the input?

Input: A solution is given to the following problem: how to compute themultiplicity, or more generally the Hilbert function, at a point on a Schubertvariety in an orthogonal Grassmannian. Standard monomial theory is applied totranslate the problem from geometry to combinatorics. The solution of theresulting combinatorial problem forms the bulk of the paper. This approach hasbeen followed earlier to solve the same problem for the Grassmannian and thesymplectic Grassmannian.  As an application, we present an interpretation of the multiplicity as thenumber of non-intersecting lattice paths of a certain kind.  Taking the Schubert variety to be of a special kind and the point to be the"identity coset," our problem specializes to a problem about Pfaffian idealstreatments of which by different methods exist in the literature. Alsoavailable in the literature is a geometric solution when the point is a"generic singularity."


Instruction: what is the prompt that generates the input?

Input: In this paper we suggest a theoretical method based on the statisticalmechanics for treating the alpha-helix-random coil transition in alaninepolypeptides. We consider this process as a first-order phase transition anddevelop a theory which is free of model parameters and is based solely onfundamental physical principles. It describes essential thermodynamicalproperties of the system such as heat capacity, the phase transitiontemperature and others from the analysis of the polypeptide potential energysurface calculated as a function of two dihedral angles, responsible for thepolypeptide twisting. The suggested theory is general and with somemodification can be applied for the description of phase transitions in othercomplex molecular systems (e.g. proteins, DNA, nanotubes, atomic clusters,fullerenes).


Instruction: what is the prompt that generates the input?

Input: Let M be a symplectic-toric manifold of dimension at least four. This paperinvestigates the so called symplectic ball packing problem in the toralequivariant setting. We show that the set of toric symplectic ball packings ofM admits the structure of a convex polytope. Previous work of the first authorshows that up to equivalence, only CP^1 x CP^1 and CP^2 admit density onepackings when n=2 and only CP^n admits density one packings when n>2. Incontrast, we show that for a fixed n>=2 and each r in (0, 1), there areuncountably many inequivalent 2n-dimensional symplectic-toric manifolds with amaximal toric packing of density r. This result follows from a general analysisof how the densities of maximal packings change while varying a givensymplectic-toric manifold through a family of symplectic-toric manifolds thatare equivariantly diffeomorphic but not equivariantly symplectomorphic.


Instruction: what is the prompt that generates the input?

Input: Astronomy can never be a hard core physics discipline, because the Universeoffers no control experiment, i.e. with no independent checks it is bound to behighly ambiguous and degenerate. Thus e.g. while superluminal motion can beexplained by Special Relativity. data on the former can never on their own beused to establish the latter. This is why traditionally astrophysicists havebeen content with (and proud of) their ability to use known physical laws andprocesses established in the laboratory to explain celestial phenomena.Cosmology is not even astrophysics: all the principal assumptions in this fieldare unverified (or unverifiable) in the laboratory, and researchers are quitecomfortable with inventing unknowns to explain the unknown. How then could,after fifty years of failed attempt in finding dark matter, the fields of darkmatter {\it and now} dark energy have become such lofty priorities in astronomyfunding, to the detriment of all other branches of astronomy? I demonstrate inthis article that while some of is based upon truth, at least just as much of$\Lambda$CDM cosmology has been propped by a paralyzing amount of propagandawhich suppress counter evidence and subdue competing models. The recent WMAP3paper of Spergel et al (2007) will be used as case in point on selectivecitation. I also show that when all evidence are taken into account, two of thecompeting models that abolish dark energy and/or dark matter do not trailbehind $\Lambda$CDM by much. Given all of the above, I believe astronomy is nolonger heading towards a healthy future, unless funding agencies re-think theirmaster plans by backing away from such high a emphasis on groping in the dark.


Instruction: what is the prompt that generates the input?

Input: In recent years, the availability of highly pure stable isotopes has madepossible the investigation of the dependence of the physical properties ofcrystals, in particular semiconductors, on their isotopic composition.Following the investigation of the specific heat ($C_p$, $C_v$) of monatomiccrystals such as diamond, silicon, and germanium, similar investigations havebeen undertaken for the tetrahedral diatomic systems ZnO and GaN (wurtzitestructure), for which the effect of the mass of the cation differs from that ofthe anion. In this article we present measurements for a semiconductor withrock salt structure, namely lead sulfide. Because of the large difference inthe atomic mass of both constituents ($M_{\rm Pb}$= 207.21 and ($M_{\rmS}$=32.06 a.m.u., for the natural isotopic abundance) the effects of varyingthe cation and that of the anion mass are very different for this canonicalsemiconductor. We compare the measured temperature dependence of $C_p \approxC_v$, and the corresponding derivatives with respect to ($M_{\rm Pb}$ and$M_{\rm S}$), with \textit{\textit{ab initio}} calculations based on thelattice dynamics obtained from the local density approximation (LDA) electronicband structure. Quantitative deviations between theory and experiment areattributed to the absence of spin-orbit interaction in the ABINIT program usedfor the electronic band structure calculations.


Instruction: what is the prompt that generates the input?

Input: The favoured progenitors of long-duration gamma-ray bursts (GRBs) are rapidlyrotating Wolf-Rayet (WR) stars. However, most Galactic WR stars are slowrotators, as stellar winds are thought to remove angular momentum. This poses achallenge to the collapsar model. Recent observations indicate that GRBs occurpredominately in low metallicity (Z) environments, which may resolve theproblem: lower Z leads to less mass loss, which may inhibit angular momentumremoval, allowing WR stars to remain rotating rapidly until collapse. We wishto determine whether low Z WR stars rotate on average more rapidly thanGalactic WR stars, and perform a Very Large Telescope (VLT) linearspectropolarimetry survey of WR stars in the low Z environment of the LargeMagellanic Cloud (LMC) and compare our results with the Galactic sample. Wefind that only 2 out of 13 (i.e. 15%) of LMC WR stars show line polarizationeffects, compared to a similarly low fraction of ~15-20% for Galactic WR stars.The low incidence of line polarization effects in LMC WR stars suggests thatthe threshold metallicity where significant differences in WR rotationalproperties occur is below that of the LMC (Z ~ 0.5 Zsun), possibly constrainingGRB progenitor channels to this upper metallicity.


Instruction: what is the prompt that generates the input?

Input: Given an object over the algebraic closure Qbar of Q, there is often noreason for invariants of the corresponding holomorphic object to be preservedby the absolute Galois group Gal(Qbar/Q), and in general this is not true,although it is sometimes surprising to observe in practice. The case of coversof the projective line branched only over the points 0, 1, and infinity,through Belyi's theorem, leads to Grothendieck's dessins d'enfants program forunderstanding the absolute Galois group through its faithful action on suchcovers. This note is motivated by Catanese's question about ahigher-dimensional analogue: does the absolute Galois group act faithfully onthe deformation equivalence classes of smooth surfaces? (These equivalenceclasses are of course by definition the strongest deformation invariants.) Wegive a short proof of a weaker result: the absolute Galois group actsfaithfully on the irreducible components of the moduli space of smooth surfaces(of general type, canonically polarized). Bauer, Catanese, and Grunewald haverecently answered Catanese's original question using a different construction.


Instruction: what is the prompt that generates the input?

Input: Context: L'-band (3.8 micron) images of the Galactic Center show a largenumber of thin filaments in the mini-spiral, located west of the mini-cavityand along the inner edge of the Northern Arm. One possible mechanism that couldproduce such structures is the interaction of a central wind with themini-spiral. Additionally, we identify similar features that appear to beassociated with stars. Aims: We present the first proper motion measurements ofthe thin dust filaments observed in the central parsec around SgrA* andinvestigate possible mechanisms that could be responsible for the observedmotions. Methods: The observations have been carried out using the NACOadaptive optics system at the ESO VLT. The images have been transformed to acommon coordinate system and features of interest were extracted. Then across-correlation technique could be performed in order to determine theoffsets between the features with respect to their position in the referenceepoch. Results: We derive the proper motions of a number of filaments and 2cometary shaped dusty sources close (in projection) to SgrA*. We show that theshape and the motion of the filaments does not agree with a purely Keplerianmotion of the gas in the potential of the supermassive black hole at theposition of SgrA*. Therefore, additional mechanisms must be responsible fortheir formation and motion. We argue that the properties of the filaments areprobably related to an outflow from the disk of young mass-losing stars aroundSgrA*. In part, the outflow may originate from the black hole itself. We alsopresent some evidence and theoretical considerations that the outflow may becollimated.


Instruction: what is the prompt that generates the input?

Input: This is an overview of recent progress in constructing and studyingsuperextensions of the Landau problem of a quantum particle on a plane in theuniform magnetic field, as well as of its Haldane's $S^2$ generalization ({\tthep-th/0311159, hep-th/0404108, hep-th/0510019, hep-th/0612300}). The mainattention is paid to the planar super Landau models which are invariant underthe inhomogeneous supergroup ISU(1|1), a contraction of the supergroup SU(2|1),and provide minimal superextensions of the original Landau model. Their commonnotable feature is the presence of a hidden dynamical worldline N=2supersymmetry. It exists at the classical and quantum levels and is revealedmost naturally while passing to the new invariant inner products in the spaceof quantum states in order to make the norms of all states positive. For one ofthe planar models, the superplane Landau model, we present an off-shellworldline superfield formulation in which the N=2 supersymmetry gets manifest.


Instruction: what is the prompt that generates the input?

Input: The first-order eikonal approximation is frequently adopted in interpretingthe results of $A(e,e'p)$ measurements. Glauber calculations, for example,typically adopt the first-order eikonal approximation. We present an extensionof the relativistic eikonal approach to $A(e,e'p)$ which accounts forsecond-order eikonal corrections. The numerical calculations are performedwithin the relativistic optical model eikonal approximation. The nucleartransparency results indicate that the effect of the second-order eikonalcorrections is rather modest, even at $Q^{2} \approx 0.2$ (GeV/c)$^2$. The sameapplies to polarization observables, left-right asymmetries, and differentialcross sections at low missing momenta. At high missing momenta, however, thesecond-order eikonal corrections are significant and bring the calculations incloser agreement with the data and/or the exact results from models adoptingpartial-wave expansions.


Instruction: what is the prompt that generates the input?

Input: We investigate the behavior of the Gibbs-Shannon entropy of the stationarynonequilibrium measure describing a one-dimensional lattice gas, of L sites,with symmetric exclusion dynamics and in contact with particle reservoirs atdifferent densities. In the hydrodynamic scaling limit, L to infinity, theleading order (O(L)) behavior of this entropy has been shown by Bahadoran to bethat of a product measure corresponding to strict local equilibrium; we computethe first correction, which is O(1). The computation uses a formal expansion ofthe entropy in terms of truncated correlation functions; for this system thek-th such correlation is shown to be O(L^{-k+1}). This entropy correctiondepends only on the scaled truncated pair correlation, which describes thecovariance of the density field. It coincides, in the large L limit, with thecorresponding correction obtained from a Gaussian measure with the samecovariance.


Instruction: what is the prompt that generates the input?

Input: The theory of the dislocation motion in the periodic potential relief of thecrystal lattice (the Peierls-Nabarro barriers) is reviewed. On the basis of thekink mechanism the temperature dependence of the flow stress is described for awide class of materials. The theory of quantum mechanical dislocationtunnelling through the Peierls-Nabarro barriers is extended and compared withexperimental data on the plasticity of alkali halides, BCC and HCP metals atlow temperatures. The behavior of the flow stress at the range of athermicanomalies is modeled by changing the mechanism of the dislocation motion fromthe thermally activated hopping over the barriers to the quantum tunnellingthrough them. Some results of previous calculations are represented in a moreexplicit convenient for applications form. The pronounced effect of theswitching between the normal and the superconducting states on the flow stressof metals is explained on the basis of the change in the dissipative propertiesof the electron subsystem affecting the dislocation motion.


Instruction: what is the prompt that generates the input?

Input: We search for stellar and substellar companions of young nearby stars toinvestigate stellar multiplicity and formation of stellar and substellarcompanions. We detect common proper-motion companions of stars via multi-epochimaging. Their companionship is finally confirmed with photometry andspectroscopy. Here we report the discovery of a new co-moving (13 sigma)stellar companion ~17.8 arcsec (350 AU in projected separation) north of thenearby star HD141272 (21 pc). With EMMI/NTT optical spectroscopy we determinedthe spectral type of the companion to be M3+-0.5V. The derived spectral type aswell as the near infrared photometry of the companion are both fully consistentwith a 0.26+-0.07 Msol dwarf located at the distance of HD141272 (21 pc).Furthermore the photometry data rules out the pre-main sequence status, sincethe system is consistent with the ZAMS of the Pleiades.


Instruction: what is the prompt that generates the input?

Input: A system of one-dimensional Brownian motions (BMs) conditioned never tocollide with each other is realized as (i) Dyson's BM model, which is a processof eigenvalues of hermitian matrix-valued diffusion process in the Gaussianunitary ensemble (GUE), and as (ii) the $h$-transform of absorbing BM in a Weylchamber, where the harmonic function $h$ is the product of differences ofvariables (the Vandermonde determinant). The Karlin-McGregor formula givesdeterminantal expression to the transition probability density of absorbing BM.We show from the Karlin-McGregor formula, if the initial state is in theeigenvalue distribution of GUE, the noncolliding BM is a determinantal process,in the sense that any multitime correlation function is given by a determinantspecified by a matrix-kernel. By taking appropriate scaling limits, spatiallyhomogeneous and inhomogeneous infinite determinantal processes are derived. Wenote that the determinantal processes related with noncolliding particlesystems have a feature in common such that the matrix-kernels are expressedusing spectral projections of appropriate effective Hamiltonians. On the commonstructure of matrix-kernels, continuity of processes in time is proved andgeneral property of the determinantal processes is discussed.


Instruction: what is the prompt that generates the input?

Input: Transport properties of ultrasmall quantum dots with a single unpairedelectron are commonly modeled by the nonequilibrium Kondo model, describing theexchange interaction of a spin-1/2 local moment with two leads ofnoninteracting electrons. Remarkably, the model possesses an exact solutionwhen tuned to a special manifold in its parameter space known as the Toulouselimit. We use the Toulouse limit to exactly calculate the adiabatically pumpedspin current in the Kondo regime. In the absence of both potential scatteringand a voltage bias, the instantaneous charge current is strictly zero for ageneric Kondo model. However, a nonzero spin current can be pumped through thesystem in the presence of a finite magnetic field, provided the spin couplesasymmetrically to the two leads. Tunneling through a Kondo impurity thus offersa natural mechanism for generating a pure spin current. We show, in particular,that one can devise pumping cycles along which the average spin pumped percycle is closely equal to $\hbar$. By analogy with Brouwer's formula fornoninteracting systems with two driven parameters, the pumped spin current isexpressed as a geometrical property of a scattering matrix. However, therelevant %Alex: I replaced topological with geometrical in the sentence abovescattering matrix that enters the formulation pertains to the Majorana fermionsthat appear at the Toulouse limit rather than the physical electrons that carrythe current. These results are obtained by combining the nonequilibrium KeldyshGreen function technique with a systematic gradient expansion, explicitlyexposing the small parameter controlling the adiabatic limit.


Instruction: what is the prompt that generates the input?

Input: We consider a simple Newtonian model of a steady accretion disk around ablack hole. The model is based on height-integrated hydrodynamic equations,alpha-viscosity, and a pseudo-Newtonian potential that results in an innermoststable circular orbit (ISCO) that closely approximates the one predicted by GR.We find that the hydrodynamic models exhibit increasing deviations from thestandard disk model of Shakura & Sunyaev as disk thickness H/R or the value ofalpha increases. The latter is an analytical model in which the viscous torqueis assumed to vanish at the ISCO. We consider the implications of the resultsfor attempts to estimate black hole spin by using the standard disk model tofit continuum spectra of black hole accretion disks. We find that the error inthe spin estimate is quite modest so long as H/R < 0.1 and alpha < 0.2. Atworst the error in the estimated value of the spin parameter is 0.1 for anon-spinning black hole; the error is much less for a rapidly spinning hole. Wealso consider the density and disk thickness contrast between the gas in thedisk and that inside the ISCO. The contrast needs to be large if black holespin is to be successfully estimated by fitting the relativistically-broadenedX-ray line profile of fluorescent iron emission from reflection off anaccretion disk. In our hydrodynamic models, the contrast in density andthickness is low when H/R>0.1, sugesting that the iron line technique may bemost reliable in extemely thin disks. We caution that these results have beenobtained with a viscous hydrodynamic model and need to be confirmed with MHDsimulations of radiatively cooled thin disks.


Instruction: what is the prompt that generates the input?

Input: We present experimental measurements of photodesorption from ices ofastrophysical relevance. Layers of benzene and water ice were irradiated with alaser tuned to an electronic transition in the benzene molecule. Thetranslational energy of desorbed molecules was measured by time-of-flight (ToF)mass spectrometry. Three distinct photodesorption processes were identified - adirect adsorbate-mediated desorption producing benzene molecules with atranslational temperature of around 1200 K, an indirect adsorbate-mediateddesorption resulting in water molecules with a translational temperature ofaround 450 K, and a substrate-mediated desorption of both benzene and waterproducing molecules with translational temperatures of around 530 K and 450 Krespectively. The translational temperature of each population of desorbedmolecules is well above the temperature of the ice matrix. The implications forgas-phase chemistry in the interstellar medium are discussed.


Instruction: what is the prompt that generates the input?

Input: We present the results of a visible spectroscopic and photometric survey ofJupiter Trojans belonging to different dynamical families carried out at theESO-NTT telescope. We obtained data on 47 objects, 23 belonging to the L5 swarmand 24 to the L4 one. These data together with those already published byFornasier et al. (2004a) and Dotto et al. (2006), constitute a total sample ofvisible spectra for 80 objects. The survey allows us to investigate sixfamilies (Aneas, Anchises, Misenus, Phereclos, Sarpedon, Panthoos) in the L5cloud and four L4 families (Eurybates, Menelaus, 1986 WD and 1986 TS6). Thesample that we measured is dominated by D--type asteroids, with the exceptionof the Eurybates family in the L4 swarm, where there is a dominance of C- andP-type asteroids. All the spectra that we obtained are featureless with theexception of some Eurybates members, where a drop--off of the reflectance isdetected shortward of 5200 A. Similar features are seen in main belt C-typeasteroids and commonly attributed to the intervalence charge transfertransition in oxidized iron. Our sample comprises fainter and smaller Trojansas compared to the literature's data and allows us to investigate theproperties of objects with estimated diameter smaller than 40--50 km. Theanalysis of the spectral slopes and colors versus the estimated diameters showsthat the blue and red objects have indistinguishable size distribution. Weperform a statistical investigation of the Trojans's spectra propertydistributions as a function of their orbital and physical parameters, and incomparison with other classes of minor bodies in the outer Solar System.Trojans at lower inclination appear significantly bluer than those at higherinclination, but this effect is strongly driven by the Eurybates family.


Instruction: what is the prompt that generates the input?

Input: We report the discovery of 14 quasars in the vicinity of HE2347-4342, one ofthe two quasars whose intergalactic HeII forest has been resolved with FUSE. Byanalysing the HI and the HeII opacity variations separately, no transverseproximity effect is detected near three foreground quasars of HE2347-4342:QSOJ23503-4328 (z=2.282, $\vartheta=3.59$ arcmin), QSOJ23500-4319 (z=2.302,$\vartheta=8.77$ arcmin) and QSOJ23495-4338 (z=2.690, $\vartheta=16.28$arcmin). This is primarily due to line contamination and overdensities probablycreated by large-scale structure. By comparing the HI absorption and thecorresponding HeII absorption, we estimated the fluctuating spectral shape ofthe extragalactic UV radiation field along this line of sight. We find that theUV spectral shape near HE2347-4342 and in the projected vicinity of the threeforeground quasars is statistically harder than expected from UV backgroundmodels dominated by quasars. In addition, we find three highly ionised metalline systems near the quasars. However, they do not yield further constraintson the shape of the ionising field. We conclude that the foreground quasarsshow a transverse proximity effect that is detectable as a local hardening ofthe UV radiation field, although the evidence is strongest for QSOJ23495-4338.Thus, the relative spectral hardness traces the proximity effect also inoverdense regions prohibiting the traditional detection in the HI forest.Furthermore, we emphasise that softening of quasar radiation by radiativetransfer in the intergalactic medium is important to understand the observedspectral shape variations. From the transverse proximity effect ofQSOJ23495-4338 we obtain a lower limit on the quasar lifetime of ~25 Myr.


Instruction: what is the prompt that generates the input?

Input: In almost all structure formation models, primordial perturbations arecreated within a homogeneous and isotropic universe, like the one we observe.Because their ensemble averages inherit the symmetries of the spacetime inwhich they are seeded, cosmological perturbations then happen to bestatistically isotropic and homogeneous. Certain anomalies in the cosmicmicrowave background on the other hand suggest that perturbations do notsatisfy these statistical properties, thereby challenging perhaps ourunderstanding of structure formation. In this article we relax this tension. Weshow that if the universe contains an appropriate triad of scalar fields withspatially constant but non-zero gradients, it is possible to generatestatistically anisotropic and inhomogeneous primordial perturbations, eventhough the energy momentum tensor of the triad itself is invariant undertranslations and rotations.


Instruction: what is the prompt that generates the input?

Input: We study how to incorporate CP violation in the Froggatt--Nielsen (FN)mechanism. To this end, we introduce non-renormalizable interactions with aflavor democratic structure to the fermion mass generation sector. It is foundthat at least two iso-singlet scalar fields with imposed a discrete symmetryare necessary to generate CP violation due to the appearance of the relativephase between their vacuum expectation values.  In the simplest model, ratios of quark masses and theCabibbo-Kobayashi-Maskawa (CKM) matrix including the CP violating phase aredetermined by the CKM element |V_{us}| and the ratio of two vacuum expectationvalues R=|R|e^{i*alpha} (a magnitude and a phase). It is demonstrated how theangles phi_i (i=1--3) of the unitarity triangle and the CKM off-diagonalelements |V_{ub}| and |V_{cb}| are predicted as a function of |V_{us}|, |R| and\alpha. Although the predicted value of the CP violating phase does not agreewith the experimental data within the simplest model, the basic idea of ourscenario would be promising to construct a more realistic model of flavor andCP violation.


Instruction: what is the prompt that generates the input?

Input: Let $f\in L_{2\pi}$ be a real-valued even function with its Fourier series $\frac{a_{0}}{2}+\sum_{n=1}^{\infty}a_{n}\cos nx,$ and let $S_{n}(f,x), n\geq1,$ be the $n$-th partial sum of the Fourier series. It is well-known that ifthe nonnegative sequence $\{a_{n}\}$ is decreasing and $\lim\limits_{n\to\infty}a_{n}=0$, then $$ \lim\limits_{n\to \infty}\Vert f-S_{n}(f)\Vert_{L}=0{if and only if} \lim\limits_{n\to \infty}a_{n}\log n=0. $$ We weaken themonotone condition in this classical result to the so-called mean value boundedvariation ($MVBV$) condition. The generalization of the above classical resultin real-valued function space is presented as a special case of the main resultin this paper which gives the $L^{1}$% -convergence of a function $f\inL_{2\pi}$ in complex space. We also give results on $L^{1}$-approximation of afunction $f\in L_{2\pi}$ under the $% MVBV$ condition.


Instruction: what is the prompt that generates the input?

Input: Rapidly oscillating potentials with a vanishing time average have been usedfor a long time to trap charged particles in source-free regions. It has beenargued that the motion of a particle in such a potential can be approximatelydescribed by a time independent effective potential, which does not depend uponthe initial phase of the oscillating potential. However, here we show that themotion of a particle and its trapping condition significantly depend upon thisinitial phase for arbitrarily high frequencies of the potential's oscillation.We explain this novel phenomenon by showing that the motion of a particle isdetermined by the effective potential stated in the literature only if itsinitial conditions are transformed according to a transformation which we showto significantly depend on the potential's initial phase for arbitrarily highfrequencies. We confirm our theoretical findings by numerical simulations.Further, we demonstrate that the found phenomenon offers new ways to manipulatethe dynamics of particles which are trapped by rapidly oscillating potentials.Finally, we propose a simple experiment to verify the theoretical findings ofthis work.


Instruction: what is the prompt that generates the input?

Input: The HARPS high-resolution high-accuracy spectrograph is offered to theastronomical community since the second half of 2003. Since then, we have beenusing this instrument for monitoring radial velocities of a large sample ofSolar-type stars (~1400 stars) in order to search for their possible low-masscompanions. Amongst the goals of our survey, one is to significantly increasethe number of detected extra-solar planets in a volume-limited sample toimprove our knowledge of their orbital elements distributions and thus obtainbetter constraints for planet-formation models.  In this paper, we present the HARPS radial-velocity data and orbitalsolutions for 3 Solar-type stars: HD 100777, HD 190647, and HD 221287. Theradial-velocity data of HD 100777 is best explained by the presence of a 1.1M_Jup planetary companion on a 384--day eccentric orbit (e=0.36). The orbitalfit obtained for the slightly evolved star HD 190647 reveals the presence of along-period (P=1038 d) 1.9 M_Jup planetary companion on a moderately eccentricorbit (e=0.18). HD 221287 is hosting a 3.1 M_Jup planet on a 456--day orbit.The shape of this orbit is not very well constrained because of our non-optimaltemporal coverage and because of the presence of abnormally large residuals. Wefind clues for these large residuals to result from spectral line profilevariations probably induced by stellar activity related processes.


Instruction: what is the prompt that generates the input?

Input: It is known that within the interacting electron model Hamiltonian for theone-dimensional 1/4-filled band, the singlet ground state is a Wigner crystalonly if the nearest neighbor electron-electron repulsion is larger than acritical value. We show that this critical nearest neighbor Coulomb interactionis different for each spin subspace, with the critical value decreasing withincreasing spin. As a consequence, with the lowering of temperature, there canoccur a transition from a Wigner crystal charge-ordered state to a spin-Peierlsstate that is a Bond-Charge-Density Wave with charge occupancies different fromthe Wigner crystal. This transition is possible because spin excitations fromthe spin-Peierls state in the 1/4-filled band are necessarily accompanied bychanges in site charge densities. We apply our theory to the 1/4-filled bandquasi-one-dimensional organic charge-transfer solids in general and to 2:1tetramethyltetrathiafulvalene (TMTTF) and tetramethyltetraselenafulvalene(TMTSF) cationic salts in particular. We believe that many recent experimentsstrongly indicate the Wigner crystal to Bond-Charge-Density Wave transition inseveral members of the TMTTF family. We explain the occurrence of two differentantiferromagnetic phases but a single spin-Peierls state in the generic phasediagram for the 2:1 cationic solids. The antiferromagnetic phases can haveeither the Wigner crystal or the Bond-Charge-Spin-Density Wave chargeoccupancies. The spin-Peierls state is always a Bond-Charge-Density Wave.


Instruction: what is the prompt that generates the input?

Input: Numerical simulations of Milky-Way size Cold Dark Matter (CDM) halos predicta steeply rising mass function of small dark matter subhalos and a substructurecount that greatly outnumbers the observed satellites of the Milky Way. Severalproposed explanations exist, but detailed comparison between theory andobservation in terms of the maximum circular velocity (Vmax) of the subhalos ishampered by the fact that Vmax for satellite halos is poorly constrained. Wepresent comprehensive mass models for the well-known Milky Way dwarfsatellites, and derive likelihood functions to show that their masses within0.6 kpc (M_0.6) are strongly constrained by the present data. We show that theM_0.6 mass function of luminous satellite halos is flat between ~ 10^7 and 10^8M_\odot. We use the ``Via Lactea'' N-body simulation to show that the M_0.6mass function of CDM subhalos is steeply rising over this range. We rule outthe hypothesis that the 11 well-known satellites of the Milky Way are hosted bythe 11 most massive subhalos. We show that models where the brightestsatellites correspond to the earliest forming subhalos or the most massiveaccreted objects both reproduce the observed mass function. A similar analysiswith the newly-discovered dwarf satellites will further test these scenariosand provide powerful constraints on the CDM small-scale power spectrum and warmdark matter models.


Instruction: what is the prompt that generates the input?

Input: We study the intersection points of a fixed planar curve $\Gamma$ with thenodal set of a translationally invariant and isotropic Gaussian random field$\Psi(\bi{r})$ and the zeros of its normal derivative across the curve. Theintersection points form a discrete random process which is the object of thisstudy. The field probability distribution function is completely specified bythe correlation $G(|\bi{r}-\bi{r}'|) = <\Psi(\bi{r}) \Psi(\bi{r}')>$.  Given an arbitrary $G(|\bi{r}-\bi{r}'|)$, we compute the two pointcorrelation function of the point process on the line, and derive otherstatistical measures (repulsion, rigidity) which characterize the short andlong range correlations of the intersection points. We use these statisticalmeasures to quantitatively characterize the complex patterns displayed byvarious kinds of nodal networks. We apply these statistics in particular tonodal patterns of random waves and of eigenfunctions of chaotic billiards. Ofspecial interest is the observation that for monochromatic random waves, thenumber variance of the intersections with long straight segments grows like $L\ln L$, as opposed to the linear growth predicted by the percolation model,which was successfully used to predict other long range nodal properties ofthat field.


Instruction: what is the prompt that generates the input?

Input: I apply a two-step density-matrix renormalization group method to theanisotropic two-dimensional Hubbard model. As a prelude to this study, Icompare the numerical results to the exact one for the tight-binding model. Ifind a ground-state energy which agrees with the exact value up to four digitsfor systems as large as $24 \times 25$. I then apply the method to theinteracting case. I find that for strong Hubbard interaction, the ground-stateis dominated by magnetic correlations.  These correlations are robust even in the presence of strong frustration.Interchain pair tunneling is negligible in the singlet and triplet channels andit is not enhanced by frustration. For weak Hubbard couplings, interchainnon-local singlet pair tunneling is enhanced and magnetic correlations arestrongly reduced. This suggests a possible superconductive ground state.


Instruction: what is the prompt that generates the input?

Input: NGC 7679 is a nearby luminous infrared Sy2 galaxy in which starburst and AGNactivities co-exist. The ionization structure is maintained by both the AGNpower-law continuum and starburst. The galaxy is a bright X-ray sourcepossessing a low X-ray column density N_H < 4 x 10^20 cm^{-2}. The Compton-thinnature of such unabsorbed objects infers that the simple formulation of theUnified model for SyGs is not applicable in their case. The main goal of thisarticle is to investigate both gas distribution and ionization structure in thecircumnuclear region of NGC 7679 in search for the presence of a hidden Sy1nucleus, using the [O III] 5007 luminosity as a tracer of AGN activity. The [OIII] 5007 image of the NGC 7679 shows elliptical isophotes extended along thePA ~ 80 deg in the direction to the counterpart galaxy NGC 7682. The maximum ofionization by the AGN power-law continuum traced by [O III] 5007/Halpha ratiois displaced by ~ 13 arcsec eastward from the nucleus. We conclude that thedust and gas in the high ionization direction has a direct view to the centralAGN engine. This possibly results in dust/star-formation decay. A largefraction of the unabsorbed Compton-thin Sy2s with [O III] luminosity > 10^41erg s^{-1} possesses a hidden AGN source (abridged).


Instruction: what is the prompt that generates the input?

Input: Based on our sample of 10095 galaxies with bulge-disc decompositions wederive the empirical B-band internal attenuation--inclination relation forgalaxy discs and their associated central bulges. Our results agree well withthe independently derived dust models of Tuffs et al., leading to a directconstraint on the mean opacity of spiral discs of Tau_B^f = 3.8 +/- 0.7(central face-on B-band opacity). Depending on inclination, the B-bandattenuation correction varies from 0.2 -- 1.1 mag for discs and from 0.8 -- 2.6mag for bulges. We find that, overall, 37 per cent of all B-band photonsproduced in discs in the nearby universe are absorbed by dust, a figure thatrises to 71 per cent for bulge photons. The severity of internal dustextinction is such that one must incorporate internal dust corrections in alloptical studies of large galaxy samples. This is particularly pertinent foroptical HST comparative evolutionary studies as the dust properties will alsobe evolving. We use the new results to revise our recent estimates of thespheroid and disc luminosity functions. From our best fitting dust models wederive a redshift zero cosmic dust density of rho_{dust} ~ (5.3 +/- 1.7) x10^5, h M_{odot} Mpc^-3. This implies that (0.0083 +/- 0.0027), h per cent ofthe baryons in the Universe are in the form of dust and (11.9 +/- 1.7), h percent (Salpeter-`lite' IMF) are in the form of stars (~58 per cent reside ingalaxy discs, ~10 per cent in red elliptical galaxies, ~29 per cent inclassical galaxy bulges and the remainder in low luminosity blue spheroidsystems/components). [Abridged]