The baryonic Tully-Fisher relation for different velocity definitions and implications for galaxy angular momentum

We study the baryonic Tully-Fisher relation (BTFR) at z=0 using 153 galaxies from the SPARC sample. We consider different definitions of the characteristic velocity from HI and H-alpha rotation curves, as well as HI line-widths from single-dish observations. We reach the following results: (1) The tightest BTFR is given by the mean velocity along the flat part of the rotation curve. The orthogonal intrinsic scatter is extremely small (6%) and the best-fit slope is 3.85+/-0.09, but systematic uncertainties may drive the slope from 3.5 to 4.0. Other velocity definitions lead to BTFRs with systematically higher scatters and shallower slopes. (2) We provide statistical relations to infer the flat rotation velocity from HI line-widths or less extended rotation curves (like H-alpha and CO data). These can be useful to study the BTFR from large HI surveys or the BTFR at high redshifts. (3) The BTFR is more fundamental than the relation between angular momentum and galaxy mass (the Fall relation). The Fall relation has about 7 times more scatter than the BTFR, which is merely driven by the scatter in the mass-size relation of galaxies. The BTFR is already the "fundamental plane" of galaxy discs: no value is added with a radial variable as a third parameter.Comment: 12 pages, 6 figures, accepted for publication in MNRA

A programme to determine the exact interior of any connected digital picture

Region filling is one of the most important and fundamental operations in computer graphics and image processing. Many filling algorithms and their implementations are based on the Euclidean geometry, which are then translated into computational models moving carelessly from the continuous to the finite discrete space of the computer. The consequences of this approach is that most implementations fail when tested for challenging degenerate and nearly degenerate regions. We present a correct integer-only procedure that works for all connected digital pictures. It finds all possible interior points, which are then displayed and stored in a locating matrix. Namely, we present a filling and locating procedure that can be used in computer graphics and image processing applications

Using compression to identify acronyms in text

Text mining is about looking for patterns in natural language text, and may be defined as the process of analyzing text to extract information from it for particular purposes. In previous work, we claimed that compression is a key technology for text mining, and backed this up with a study that showed how particular kinds of lexical tokens---names, dates, locations, etc.---can be identified and located in running text, using compression models to provide the leverage necessary to distinguish different token types (Witten et al., 1999)Comment: 10 pages. A short form published in DCC200

A Study of NK Landscapes' Basins and Local Optima Networks

We propose a network characterization of combinatorial fitness landscapes by adapting the notion of inherent networks proposed for energy surfaces (Doye, 2002). We use the well-known family of $NK$ landscapes as an example. In our case the inherent network is the graph where the vertices are all the local maxima and edges mean basin adjacency between two maxima. We exhaustively extract such networks on representative small NK landscape instances, and show that they are 'small-worlds'. However, the maxima graphs are not random, since their clustering coefficients are much larger than those of corresponding random graphs. Furthermore, the degree distributions are close to exponential instead of Poissonian. We also describe the nature of the basins of attraction and their relationship with the local maxima network.Comment: best paper nominatio

Relative Convex Hull Determination from Convex Hulls in the Plane

A new algorithm for the determination of the relative convex hull in the plane of a simple polygon A with respect to another simple polygon B which contains A, is proposed. The relative convex hull is also known as geodesic convex hull, and the problem of its determination in the plane is equivalent to find the shortest curve among all Jordan curves lying in the difference set of B and A and encircling A. Algorithms solving this problem known from Computational Geometry are based on the triangulation or similar decomposition of that difference set. The algorithm presented here does not use such decomposition, but it supposes that A and B are given as ordered sequences of vertices. The algorithm is based on convex hull calculations of A and B and of smaller polygons and polylines, it produces the output list of vertices of the relative convex hull from the sequence of vertices of the convex hull of A.Comment: 15 pages, 4 figures, Conference paper published. We corrected two typing errors in Definition 2: $I_S$ has to be defined based on $O_S$, and $I_E$ has to be defined based on $O_E$ (not just using $O$). These errors appeared in the text of the original conference paper, which also contained the pseudocode of an algorithm where $I_S$ and $I_E$ appeared as correctly define

A topological approach for segmenting human body shape

Segmentation of a 3D human body, is a very challenging problem in applications exploiting human scan data. To tackle this problem, the paper proposes a topological approach based on the discrete Reeb graph (DRG) which is an extension of the classical Reeb graph to handle unorganized clouds of 3D points. The essence of the approach concerns detecting critical nodes in the DRG, thereby permitting the extraction of branches that represent parts of the body. Because the human body shape representation is built upon global topological features that are preserved so long as the whole structure of the human body does not change, our approach is quite robust against noise, holes, irregular sampling, frame change and posture variation. Experimental results performed on real scan data demonstrate the validity of our method

Configurational temperatures and interactions in charge-stabilized colloid

We demonstrate that the configurational temperature formalism can be derived from the classical hypervirial theorem, and introduce a hierarchy of hyperconfigurational temperature definitions, which are particularly well suited for experimental studies. We then use these analytical tools to probe the electrostatic interactions in monolayers of charge-stabilized colloidal spheres confined by parallel glass surfaces. The configurational and hyperconfigurational temperatures, together with a novel thermodynamic sum rule, provide previously lacking self-consistency tests for interaction measurements based on digital video microscopy, and thereby cast new light on controversial reports of confinement-induced like-charge attractions. We further introduce a new method for measuring the pair potential directly that uses consistency of the configurational and hyperconfigurational temperatures as a set of constraints for a model-free search.Comment: 15 pages, 12 figures, submitted to J. Chem. Phy