The Power of Non-Determinism in Higher-Order Implicit Complexity

We investigate the power of non-determinism in purely functional programming languages with higher-order types. Specifically, we consider cons-free programs of varying data orders, equipped with explicit non-deterministic choice. Cons-freeness roughly means that data constructors cannot occur in function bodies and all manipulation of storage space thus has to happen indirectly using the call stack. While cons-free programs have previously been used by several authors to characterise complexity classes, the work on non-deterministic programs has almost exclusively considered programs of data order 0. Previous work has shown that adding explicit non-determinism to cons-free programs taking data of order 0 does not increase expressivity; we prove that this - dramatically - is not the case for higher data orders: adding non-determinism to programs with data order at least 1 allows for a characterisation of the entire class of elementary-time decidable sets. Finally we show how, even with non-deterministic choice, the original hierarchy of characterisations is restored by imposing different restrictions.Comment: pre-edition version of a paper accepted for publication at ESOP'1

Identification of a novel high molecular weight protein preferentially expressed by sinusoidal endothelial cells in normal human tissues

Mouse mAb MS-1, raised against human spleen, detects an endothelial cell antigen abundantly expressed by the sinusoidal endothelia of spleen, lymph node, liver, and adrenal cortex, but absent from nonsinusoidal continuous endothelia in these organs. Immunoelectron microscopy of splenic tissue demonstrates that the MS-1 antigen is predominantly deposited at zones of intercellular contact between adjacent sinusoidal endothelial cells. mAb MS-1 also reacts with a variable proportion of high endothelial venules in tonsil, but not in other lymphoid tissues, and with an interstitial dendritic cell population most abundant in placenta. mAb MS-1 does not react with cultured resting or mediator-activated human umbilical vein endothelial cells, dermal fibroblasts, peripheral blood mononuclear cells, or the cell lines U937, HL-60, K562 or Mo7E; it does react with the primitive myeloid cell line KG-1. mAb MS-1 immunoprecipitates a major protein of 215 kD and minor proteins of 320 and 120 kD from splenic extracts as analyzed by SDS-PAGE with reduction. These proteins are soluble in aqueous buffers. Immunoprecipitation from KG-1 cell lysates detects four proteins of 280, 300, 205, and 120 kD; the 300-, 205-, and 120-kD species, presumably corresponding to the 320-, 215-, and 120-kD species in spleen, respectively, are secreted into the media. Under nonreducing conditions, immunoprecipitates from KG-1 cell lysates or conditioned media contain one predominant 300-kD species; upon isolation and reduction, this 300-kD species separates into the previously observed 300-, 205-, and 120-kD species. Pulse-chase experiments and limited proteolysis peptide mapping suggest that the 280-kD species is a precursor of the mature 300-kD species which may be subsequently cleaved to yield the 205- and 120-kD species. Because of its size, solubility and expression pattern, the antigen recognized by mAb MS-1 is likely to be an extracellular matrix protein utilized by endothelial cells of contorted, large caliber, or leaky microvessels that lack a well-formed basement membrane

Cluster expansions in dilute systems: applications to satisfiability problems and spin glasses

We develop a systematic cluster expansion for dilute systems in the highly dilute phase. We first apply it to the calculation of the entropy of the K-satisfiability problem in the satisfiable phase. We derive a series expansion in the control parameter, the average connectivity, that is identical to the one obtained by using the replica approach with a replica symmetric ({\sc rs}) {\it Ansatz}, when the order parameter is calculated via a perturbative expansion in the control parameter. As a second application we compute the free-energy of the Viana-Bray model in the paramagnetic phase. The cluster expansion allows one to compute finite-size corrections in a simple manner and these are particularly important in optimization problems. Importantly enough, these calculations prove the exactness of the {\sc rs} {\it Ansatz} below the percolation threshold and might require its revision between this and the easy-to-hard transition.Comment: 21 pages, 7 figs, to appear in Phys. Rev.

Optimisation problems and replica symmetry breaking in finite connectivity spin-glasses

A formalism capable of handling the first step of hierarchical replica symmetry breaking in finite-connectivity models is introduced. The emerging order parameter is claimed to be a probability distribution over the space of field distributions (or, equivalently magnetisation distributions) inside the cluster of states. The approach is shown to coincide with the previous works in the replica symmetric case and in the two limit cases m=0,1 where m is Parisi's break-point. As an application to the study of optimization problems, the ground-state properties of the random 3-Satisfiability problem are investigated and we present a first RSB solution improving replica symmetric results.Comment: 16 pages Revtex file, 1 figure; amended version with two new appendices; to be published in J.Phys.

Spatially Resolved Kinematics of an Ultra-Compact Dwarf Galaxy

We present the internal kinematics of UCD3, the brightest known ultra-compact dwarf galaxy (UCD) in the Fornax cluster, making this the first UCD with spatially resolved spectroscopy. Our study is based on seeing-limited observations obtained with the ARGUS Integral Field Unit of the VLT/FLAMES spectrograph under excellent seeing conditions (0.5 - 0.67 arcsec FWHM). The velocity field of UCD3 shows the signature of weak rotation, comparable to that found in massive globular clusters. Its velocity dispersion profile is fully consistent with an isotropic velocity distribution and the assumption that mass follows the light distribution obtained from Hubble Space Telescope imaging. In particular, there is no evidence for the presence of an extended dark matter halo contributing a significant (>~33 per cent within R < 200 pc) mass fraction, nor for a central black hole more massive than ~5 per cent of the UCD's mass. While this result does not exclude a galaxian origin for UCD3, we conclude that its internal kinematics are fully consistent with it being a massive star cluster.Comment: 5 pages, 3 figures; accepted for publication in MNRAS Letter

The Nature of UCDs: Internal Dynamics from an Expanded Sample and Homogeneous Database

We have obtained high-resolution spectra of 23 ultra-compact dwarf galaxies (UCDs) in the Fornax cluster with -10.4>M_V>-13.5 mag (10^6<M/M_*<10^8), using FLAMES/Giraffe at the VLT. This is the largest homogeneous data set of UCD internal dynamics assembled to date. We derive dynamical M/L ratios for 15 UCDs covered by HST imaging. In the M_V-sigma plane, UCDs with M_V<-12 mag are consistent with the extrapolated Faber-Jackson relation for luminous ellipticals, while fainter UCDs are closer to the extrapolated globular cluster (GC) relation. At a given metallicity, Fornax UCDs have on average 30-40% lower M/L ratios than Virgo UCDs, suggesting possible differences in age or dark matter content between Fornax and Virgo UCDs. For our sample of Fornax UCDs we find no significant correlation between M/L ratio and mass. We combine our data with available M/L ratio measurements of compact stellar systems with 10^4<M/M_*<10^8, and normalise all M/L estimates to solar metallicity. We find that UCDs (M > 2*10^6 M_*) have M/L ratios twice as large as GCs (M < 2*10^6 M_*). We show that stellar population models tend to under-predict dynamical M/L ratios of UCDs and over-predict those of GCs. Considering the scaling relations of stellar spheroids, UCDs align well along the 'Fundamental Manifold', constituting the small-scale end of the galaxy sequence. The alignment for UCDs is especially clear for r_e >~ 7 pc, which corresponds to dynamical relaxation times that exceed a Hubble time. In contrast, GCs exhibit a broader scatter and do not appear to align along the manifold. We argue that UCDs are the smallest dynamically un-relaxed stellar systems, with M > 2*10^6 M_* and 7<r_e<100 pc. Future studies should aim at explaining the elevated M/L ratios of UCDs and the environmental dependence of their properties.Comment: 17 pages, 14 figures, accepted for publication in A&A. V3 taking into account proof corrections: Table 3 radial velocity entries corrected by heliocentric correction, updated sigma entries in Table 5 for a few CenA sources, updated references for G1 and omega Ce

Statistical mechanics of the random K-SAT model

The Random K-Satisfiability Problem, consisting in verifying the existence of an assignment of N Boolean variables that satisfy a set of M=alpha N random logical clauses containing K variables each, is studied using the replica symmetric framework of diluted disordered systems. We present an exact iterative scheme for the replica symmetric functional order parameter together for the different cases of interest K=2, K>= 3 and K>>1. The calculation of the number of solutions, which allowed us [Phys. Rev. Lett. 76, 3881 (1996)] to predict a first order jump at the threshold where the Boolean expressions become unsatisfiable with probability one, is thoroughly displayed. In the case K=2, the (rigorously known) critical value (alpha=1) of the number of clauses per Boolean variable is recovered while for K>=3 we show that the system exhibits a replica symmetry breaking transition. The annealed approximation is proven to be exact for large K.Comment: 34 pages + 1 table + 8 fig., submitted to Phys. Rev. E, new section added and references update

Gas Accretion Traced in Absorption in Galaxy Spectroscopy

The positive velocity shift of absorption transitions tracing diffuse material observed in a galaxy spectrum is an unambiguous signature of gas flow toward the host system. Spectroscopy probing, e.g., NaI D resonance lines in the rest-frame optical or MgII and FeII in the near-ultraviolet is in principle sensitive to the infall of cool material at temperatures ~ 100-10,000 K anywhere along the line of sight to a galaxy's stellar component. However, secure detections of this redshifted absorption signature have proved challenging to obtain due to the ubiquity of cool gas outflows giving rise to blueshifted absorption along the same sightlines. In this chapter, we review the bona fide detections of this phenomenon. Analysis of NaI D line profiles has revealed numerous instances of redshifted absorption observed toward early-type and/or AGN-host galaxies, while spectroscopy of MgII and FeII has provided evidence for ongoing gas accretion onto >5% of luminous, star-forming galaxies at z ~ 0.5-1. We then discuss the potentially ground-breaking benefits of future efforts to improve the spectral resolution of such studies, and to leverage spatially-resolved spectroscopy for new constraints on inflowing gas morphology.Comment: 21 pages, 7 figures. Invited review to appear in Gas Accretion onto Galaxies, Astrophysics and Space Science Library, eds. A. J. Fox & R. Dav\'e, to be published by Springe

Sparser Random 3SAT Refutation Algorithms and the Interpolation Problem:Extended Abstract

We formalize a combinatorial principle, called the 3XOR principle, due to Feige, Kim and Ofek [12], as a family of unsatisfiable propositional formulas for which refutations of small size in any propo-sitional proof system that possesses the feasible interpolation property imply an efficient deterministic refutation algorithm for random 3SAT with n variables and Ω(n1.4) clauses. Such small size refutations would improve the state of the art (with respect to the clause density) efficient refutation algorithm, which works only for Ω(n1.5) many clauses [13]. We demonstrate polynomial-size refutations of the 3XOR principle in resolution operating with disjunctions of quadratic equations with small integer coefficients, denoted R(quad); this is a weak extension of cutting planes with small coefficients. We show that R(quad) is weakly autom-atizable iff R(lin) is weakly automatizable, where R(lin) is similar to R(quad) but with linear instead of quadratic equations (introduced in [25]). This reduces the problem of refuting random 3CNF with n vari-ables and Ω(n1.4) clauses to the interpolation problem of R(quad) and to the weak automatizability of R(lin)

An XMM-Newton search for X-ray sources in the Fornax dwarf galaxy

We report the results of a deep archive XMM-Newton observation of the Fornax spheroidal galaxy that we analyzed with the aim of fully characterizing the X-ray source population (in most of the cases likely to be background active galactic nuclei) detected towards the target. A cross correlation with the available databases allowed us to find a source that may be associated with a variable star belonging to the galaxy. We also searched for X-ray sources in the vicinity of the Fornax globular clusters GC 3 and GC 4 and found two sources probably associated with the respective clusters. The deep X-ray observation was also suitable for the search of the intermediate-mass black hole (of mass $\simeq 10^{4}$ M$_{\odot}$) expected to be hosted in the center of the galaxy. In the case of Fornax, this search is extremely difficult since the galaxy centroid of gravity is poorly constrained because of the large asymmetry observed in the optical surface brightness. Since we cannot firmly establish the existence of an X-ray counterpart of the putative black hole, we put constraints only on the accretion parameters. In particular, we found that the corresponding upper limit on the accretion efficiency, with respect to the Eddington luminosity, is as low as a few $10^{-5}$.Comment: In press on Astronomy and Astrophysics. 12 Pages, colour figures on the on-line version of the pape