Public Imaging Surveys: Scientific Opportunities

The start of operation of several large-aperture telescopes has motivated several groups around the world to conduct deep large imaging surveys, complementing other wide-area but shallower surveys. A special class of imaging surveys are the public ones such as those being conducted by the ESO Imaging Survey (EIS) project established with the primary objective of providing to the ESO community large datasets from which samples can be drawn for VLT programs. To date several surveys have been carried out providing multi-passband optical data over relatively large areas to moderate depth, deep optical/infrared surveys of smaller fields as well as observations of a large number of selected stellar fields. These surveys have produced a large amount of well-defined datasets with known limits from which a variety of data products have been extracted and distributed. The goal of the present contribution is to give an overview of the EIS project, to present the end-to-end survey system being developed by this program and to highlight the effort being made to standardize procedures, to build software tools to assess the quality of the derived products and to explore the available datasets in a systematic and consistent way to search for astronomical objects of potential scientific interest.Comment: 19 pages, 9 Postscript figures, uses cl2emult.sty. Invited talk at the conference "Mining the Sky", August 2000, Garching, German

On a total function which overtakes all total recursive functions

This paper discusses a function that is frequently presented as a simile or look-alike of the so-called ``counterexample function to P=NP,'' that is, the function that collects all first instances of a problem in NP where a poly machine incorrectly `guesses' about the instance. We state and give in full detail a crucial result on the computation of Goedel numbers for some families of poly machines.Comment: LaTe

On the existence of certain total recursive functions in nontrivial axiom systems, I

We investigate the existence of a class of ZFC-provably total recursive unary functions, given certain constraints, and apply some of those results to show that, for $\Sigma_1$-sound set theory, ZFC$\not\vdash P<NP$.Comment: LaTeX, 16 pages, no figures. This paper was submitted to a major journal in the field and rejected. The referee somehow misundesrtood Corollary 3.8 and wrongly concluded that the proof had either a gap or an error. Can you find whether that error exists

A lemma on a total function defined over the Baker-Gill-Solovay set of polynomial Turing machines

If we establish that the counterexample function for P=NP, if total, overtakes all total recursive functions when extended over all Turing machines, then what happens to the same counterexample function when defined over the so-called Baker-Gill-Solovay (BGS) set of poly machines? We state and prove here a lemma that tries to answer this query.Comment: LaTe

On the consistency of P=NPP=NP with fragments of ZFC whose own consistency strength can be measured by an ordinal assignment

We formulate the $P<NP$ hypothesis in the case of the satisfiability problem as a $\Pi ^0_2$ sentence, out of which we can construct a partial recursive function $f_{\neg A}$ so that $f_{\neg A}$ is total if and only if $P < NP$. We then show that if $f_{\neg A}$ is total, then it isn't ${\cal T}$--provably total (where ${\cal T}$ is a fragment of ZFC that adequately extends PA and whose consistency is of ordinal order). Follows that the negation of $P < NP$, that is, $P = NP$, is consistent with those ${\cal T}$.Comment: LaTeX, 19 pages, no figure

Finding the optimal nets for self-folding Kirigami

Three-dimensional shells can be synthesized from the spontaneous self-folding of two-dimensional templates of interconnected panels, called nets. However, some nets are more likely to self-fold into the desired shell under random movements. The optimal nets are the ones that maximize the number of vertex connections, i.e., vertices that have only two of its faces cut away from each other in the net. Previous methods for finding such nets are based on random search and thus do not guarantee the optimal solution. Here, we propose a deterministic procedure. We map the connectivity of the shell into a shell graph, where the nodes and links of the graph represent the vertices and edges of the shell, respectively. Identifying the nets that maximize the number of vertex connections corresponds to finding the set of maximum leaf spanning trees of the shell graph. This method allows not only to design the self-assembly of much larger shell structures but also to apply additional design criteria, as a complete catalog of the maximum leaf spanning trees is obtained.Comment: 6 pages, 5 figures, Supplemental Material, Source Cod

A VLT/FLAMES study of the peculiar intermediate-age Large Magellanic Cloud star cluster NGC 1846 - I. Kinematics

In this paper we present high resolution VLT/FLAMES observations of red giant stars in the massive intermediate-age Large Magellanic Cloud star cluster NGC 1846, which, on the basis of its extended main-sequence turn-off (EMSTO), possesses an internal age spread of ~300 Myr. We describe in detail our target selection and data reduction procedures, and construct a sample of 21 stars possessing radial velocities indicating their membership of NGC 1846 at high confidence. We consider high-resolution spectra of the planetary nebula Mo-17, and conclude that this object is also a member of the cluster. Our measured radial velocities allow us to conduct a detailed investigation of the internal kinematics of NGC 1846, the first time this has been done for an EMSTO system. The key result of this work is that the cluster exhibits a significant degree of systemic rotation, of a magnitude comparable to the mean velocity dispersion. Using an extensive suite of Monte Carlo models we demonstrate that, despite our relatively small sample size and the substantial fraction of unresolved binary stars in the cluster, the rotation signal we detect is very likely to be genuine. Our observations are in qualitative agreement with the predictions of simulations modeling the formation of multiple populations of stars in globular clusters, where a dynamically cold, rapidly rotating second generation is a common feature. NGC 1846 is less than one relaxation time old, so any dynamical signatures encoded during its formation ought to remain present.Comment: Accepted for publication in Ap

Inverting the Achlioptas rule for explosive percolation

In the usual Achlioptas processes the smallest clusters of a few randomly chosen ones are selected to merge together at each step. The resulting aggregation process leads to the delayed birth of a giant cluster and the so-called explosive percolation transition showing a set of anomalous features. We explore a process with the opposite selection rule, in which the biggest clusters of the randomly chosen ones merge together. We develop a theory of this kind of percolation based on the Smoluchowski equation, find the percolation threshold, and describe the scaling properties of this continuous transition, namely, the critical exponents and amplitudes, and scaling functions. We show that, qualitatively, this transition is similar to the ordinary percolation one, though occurring in less connected systems.Comment: 6 pages, 2 figure

Solution of the explosive percolation quest: Scaling functions and critical exponents

Percolation refers to the emergence of a giant connected cluster in a disordered system when the number of connections between nodes exceeds a critical value. The percolation phase transitions were believed to be continuous until recently when in a new so-called "explosive percolation" problem for a competition driven process, a discontinuous phase transition was reported. The analysis of evolution equations for this process showed however that this transition is actually continuous though with surprisingly tiny critical exponents. For a wide class of representative models, we develop a strict scaling theory of this exotic transition which provides the full set of scaling functions and critical exponents. This theory indicates the relevant order parameter and susceptibility for the problem, and explains the continuous nature of this transition and its unusual properties.Comment: 15 pages, 5 figure

Critical exponents of the explosive percolation transition

In a new type of percolation phase transition, which was observed in a set of non-equilibrium models, each new connection between vertices is chosen from a number of possibilities by an Achlioptas-like algorithm. This causes preferential merging of small components and delays the emergence of the percolation cluster. First simulations led to a conclusion that a percolation cluster in this irreversible process is born discontinuously, by a discontinuous phase transition, which results in the term "explosive percolation transition". We have shown that this transition is actually continuous (second-order) though with an anomalously small critical exponent of the percolation cluster. Here we propose an efficient numerical method enabling us to find the critical exponents and other characteristics of this second order transition for a representative set of explosive percolation models with different number of choices. The method is based on gluing together the numerical solutions of evolution equations for the cluster size distribution and power-law asymptotics. For each of the models, with high precision, we obtain critical exponents and the critical point.Comment: 7 pages, 4 figure