Quicksort with unreliable comparisons: a probabilistic analysis

We provide a probabilistic analysis of the output of Quicksort when comparisons can err.Comment: 29 pages, 3 figure

Electrodeposition of Metals in Microgravity Conditions

Metal electrodeposition may introduce various morphological variations depending on the electrolytic conditions including cell configurations. For liquid electrolytes, a precise study of these deposits may be complicated by convective motion due to buoyancy. Zero-gravity (0-G) condition provided by drop shaft or parabolic flight gives a straightforward mean to avoid this effect: we present here 0-G electrodeposition experiments, which we compare to ground experiments (1-G). Two electrochemical systems were studied by laser interferometry, allowing to measure the concentration variations in the electrolyte: copper deposition from copper sulfate aqueous solution and lithium deposition from an ionic liquid containing LiTFSI. For copper, concentration variations were in good agreement with theory. For lithium, an apparent induction time was observed for the concentration evolution at 1-G: due to this induction time and to the low diffusion coefficient in ionic liquid, the concentration variations were hardly measurable in the parabolic flight 0-G periods of 20 seconds

Antireflection of an absorbing substrate by an absorbing thin film at normal incidence

An absorbing substrate of complex refractive index n2 - jk2 at wavelength λ can be coated by an absorbing thin film of complex refractive index n1 - jk1 and thickness d to achieve zero reflection at normal incidence. For given n2,k2 multiple solutions (n1,k1,d/λ) are found that correspond to infinitely many distinct antireflection layers. This is demonstrated for a Si substrate at two wavelengths (6328 and 4420 Å). The response of these absorbing antireflection layers to changes of the angle of incidence from 0 to 45° and to changes of thickness of ±10% is also determined and compared to the limting case of a nonabsorbing antireflection layer

Planar maps and continued fractions

We present an unexpected connection between two map enumeration problems. The first one consists in counting planar maps with a boundary of prescribed length. The second one consists in counting planar maps with two points at a prescribed distance. We show that, in the general class of maps with controlled face degrees, the solution for both problems is actually encoded into the same quantity, respectively via its power series expansion and its continued fraction expansion. We then use known techniques for tackling the first problem in order to solve the second. This novel viewpoint provides a constructive approach for computing the so-called distance-dependent two-point function of general planar maps. We prove and extend some previously predicted exact formulas, which we identify in terms of particular Schur functions.Comment: 47 pages, 17 figures, final version (very minor changes since v2

Antireflection of an absorbing substrate by an absorbing thin film at normal incidence

An absorbing substrate of complex refractive index n2 - jk2 at wavelength λ can be coated by an absorbing thin film of complex refractive index n1 - jk1 and thickness d to achieve zero reflection at normal incidence. For given n2,k2 multiple solutions (n1,k1,d/λ) are found that correspond to infinitely many distinct antireflection layers. This is demonstrated for a Si substrate at two wavelengths (6328 and 4420 Å). The response of these absorbing antireflection layers to changes of the angle of incidence from 0 to 45° and to changes of thickness of ±10% is also determined and compared to the limting case of a nonabsorbing antireflection layer

Electrodeposition of In2S3 buffer layer for Cu(In,Ga)Se2 solar cells

AbstractThe electrochemical deposition of In2S3 thin films was carried out from an aqueous solution of InCl3 and Na2S2O3. The effect of the potential of deposition was studied on the cell parameters of CIGSe based solar cells. The obtained films depending on the deposition potential and thickness exhibited complete substrate coverage or nanocolumnar layers. XPS measurements detected the presence of indium sulphide and hydroxide depending on the deposition parameters. Maximum photoelectric conversion efficiency of 10.2% was obtained, limited mainly by a low fill factor (56%). Further process optimization is expected to lead to efficiencies comparable to CdS buffer layers

The topological structure of scaling limits of large planar maps

We discuss scaling limits of large bipartite planar maps. If p is a fixed integer strictly greater than 1, we consider a random planar map M(n) which is uniformly distributed over the set of all 2p-angulations with n faces. Then, at least along a suitable subsequence, the metric space M(n) equipped with the graph distance rescaled by the factor n to the power -1/4 converges in distribution as n tends to infinity towards a limiting random compact metric space, in the sense of the Gromov-Hausdorff distance. We prove that the topology of the limiting space is uniquely determined independently of p, and that this space can be obtained as the quotient of the Continuum Random Tree for an equivalence relation which is defined from Brownian labels attached to the vertices. We also verify that the Hausdorff dimension of the limit is almost surely equal to 4.Comment: 45 pages Second version with minor modification

Random trees between two walls: Exact partition function

We derive the exact partition function for a discrete model of random trees embedded in a one-dimensional space. These trees have vertices labeled by integers representing their position in the target space, with the SOS constraint that adjacent vertices have labels differing by +1 or -1. A non-trivial partition function is obtained whenever the target space is bounded by walls. We concentrate on the two cases where the target space is (i) the half-line bounded by a wall at the origin or (ii) a segment bounded by two walls at a finite distance. The general solution has a soliton-like structure involving elliptic functions. We derive the corresponding continuum scaling limit which takes the remarkable form of the Weierstrass p-function with constrained periods. These results are used to analyze the probability for an evolving population spreading in one dimension to attain the boundary of a given domain with the geometry of the target (i) or (ii). They also translate, via suitable bijections, into generating functions for bounded planar graphs.Comment: 25 pages, 7 figures, tex, harvmac, epsf; accepted version; main modifications in Sect. 5-6 and conclusio

Geodesic Distance in Planar Graphs

We derive the exact generating function for planar maps (genus zero fatgraphs) with vertices of arbitrary even valence and with two marked points at a fixed geodesic distance. This is done in a purely combinatorial way based on a bijection with decorated trees, leading to a recursion relation on the geodesic distance. The latter is solved exactly in terms of discrete soliton-like expressions, suggesting an underlying integrable structure. We extract from this solution the fractal dimensions at the various (multi)-critical points, as well as the precise scaling forms of the continuum two-point functions and the probability distributions for the geodesic distance in (multi)-critical random surfaces. The two-point functions are shown to obey differential equations involving the residues of the KdV hierarchy.Comment: 38 pages, 8 figures, tex, harvmac, eps

Bioactivity and structural properties of chimeric analogs of the starfish SALMFamide neuropeptides S1 and S2

The starfish SALMFamide neuropeptides S1 (GFNSALMFamide) and S2 (SGPYSFNSGLTFamide) are the prototypical members of a family of neuropeptides that act as muscle relaxants in echinoderms. Comparison of the bioactivity of S1 and S2 as muscle relaxants has revealed that S2 is ten times more potent than S1. Here we investigated a structural basis for this difference in potency by comparing the bioactivity and solution conformations (using NMR and CD spectroscopy) of S1 and S2 with three chimeric analogs of these peptides. A peptide comprising S1 with the addition of S2's N-terminal tetrapeptide (Long S1 or LS1; SGPYGFNSALMFamide) was not significantly different to S1 in its bioactivity and did not exhibit concentration-dependent structuring seen with S2. An analog of S1with its penultimate residue substituted from S2 (S1(T); GFNSALTFamide) exhibited S1-like bioactivity and structure. However, an analog of S2 with its penultimate residue substituted from S1 (S2(M); SGPYSFNSGLMFamide) exhibited loss of S2-type bioactivity and structural properties. Collectively, our data indicate that the C-terminal regions of S1 and S2 are the key determinants of their differing bioactivity. However, the N-terminal region of S2 may influence its bioactivity by conferring structural stability in solution. Thus, analysis of chimeric SALMFamides has revealed how neuropeptide bioactivity is determined by a complex interplay of sequence and conformation