Succinct data structure for dynamic trees with faster queries

Navarro and Sadakane [TALG 2014] gave a dynamic succinct data structure for storing an ordinal tree. The structure supports tree queries in either $O(\log n/\log\log n)$ or $O(\log n)$ time, and insertion or deletion of a single node in $O(\log n)$ time. In this paper we improve the result of Navarro and Sadakane by reducing the time complexities of some queries (e.g.\ degree and level\_ancestor) from $O(\log n)$ to $O(\log n/\log\log n)$

Parameterized algorithm for 3-path vertex cover

In the 3-path vertex cover problem, the input is an undirected graph $G$ and an integer $k$. The goal is to decide whether there is a set of vertices $S$ of size at most $k$ such that every path with 3 vertices in $G$ contains at least one vertex of $S$. In this paper we give parameterized algorithm for 3-path cover whose time complexity is $O^*(1.713^k)$. Our algorithm is faster than previous algorithms for this problem

Weighted vertex cover on graphs with maximum degree 3

We give a parameterized algorithm for weighted vertex cover on graphs with maximum degree 3 whose time complexity is $O^*(1.402^t)$, where $t$ is the minimum size of a vertex cover of the input graph

Characteristic Scales in Galaxy Formation

Recent data, e.g. from SDSS and 2dF, reveal a robust bi-modality in the distribution of galaxy properties, with a characteristic transition scale at stellar mass M_*~3x10^{10} Msun (near L_*), corresponding to virial velocity V~100 km/s. Smaller galaxies tend to be blue disks of young populations. They define a "fundamental line" of decreasing surface brightness, metallicity and velocity with decreasing M_*, which extends to the smallest dwarf galaxies. Galaxies above the critical scale are dominated by red spheroids of old populations, with roughly constant high surface brightens and metallicity, and they tend to host AGNs. A minimum in the virial M/L is obtained at the same magic scale. This bi-modality can be the combined imprint of several different physical processes. On smaller scales, disks are built by cold flows, and supernova feedback is effective in regulating star formation. On larger scales, the infalling gas is heated by a virial shock and star formation can be suppressed by AGN feedback. Another feedback mechanism -- gas evaporation due to photo-ionization -- may explain the existence of totally dark halos below V~30 km/s. The standard cooling barriers are responsible for the loose upper and lower bounds for galaxies: 10 < V < 300 km/s.Comment: 10 pages, 5 figures, LaTeX (svmult.cls, physprbb.sty), to be published in ESO/USM/MPE Venice Workshop on Multiwavelength Mapping of Galaxy Formation and Evolution, eds. R. Bender and A. Renzini. Also http://phys.huji.ac.il/~dekel/scales/scales.ps.g

Cosmological Implications of Large-Scale Flows

Cosmological implications of the observed large-scale peculiar velocities are reviewed, alone or combined with redshift surveys and CMB data. The latest version of the POTENT method for reconstructing the underlying three-dimensional velocity and mass-density fields is described. The initial fluctuations and the nature of the dark matter are addressed via statistics such as bulk flow and mass power spectrum. The focus is on constraining the mass density parameter $\Omega$, directly or via the parameter $\beta$ which involves the unknown relation between galaxies and mass. The acceptable range for $\Omega$ is found to be $0.4-1.0$. The range of $\beta$ estimates is likely to reflect non-trivial features in the galaxy biasing scheme, such as scale dependence. Similar constraints on $\Omega$ and $\Lambda$ from global measures are summarized.Comment: 40 pages, 15 figures, LaTex (aaspp4.sty), to appear in the proceedings of the 3rd ESO-VLT Workshop on ``Galaxy Scaling Relations: Origins, Evolution and Applications", ed. L. da Costa (Springer

Faster parameterized algorithm for pumpkin vertex deletion set

A directed graph $G$ is called a pumpkin if $G$ is a union of induced paths with a common start vertex $s$ and a common end vertex $t$, and the internal vertices of every two paths are disjoint. We give an algorithm that given a directed graph $G$ and an integer $k$, decides whether a pumpkin can be obtained from $G$ by deleting at most $k$ vertices. The algorithm runs in $O^*(2^k)$ time

Cosmic Flows 99: Conference Summary

I address the following issues: All bulk velocity measurements (but one) are consistent with our standard gravitational instability theory. New accurate data and reconstruction methods allow high-resolution dynamical analysis nearby, revealing Virgo, Ursa Major and Fornax as attractors. Large peculiar-velocity surveys enable robust reconstruction of the dynamical fields on the Great-Attractor scale. A decomposition of the velocity field into its local and tidal components indicates the presence of big perturbations further away. Cluster velocities start exploring very large scales, revealing Coma, Shapely and other mass enhancements, and constraining a possible local Hubble bubble. Supernovae type Ia (SNIa) are very promising for cosmic flow analysis. Peculiar velocities do provide unique valuable constraints on cosmological parameters, e.g., 0.3<Omega_m<1 (95% confidence) independent of biasing. Jointly with other data they can confine other parameters such as Omega_Lambda, h, sigma_8, n, and the biasing. Nontrivial features of the biasing scheme can explain much of the span of estimates for beta. Quantitative error analysis is essential in our maturing field; every method ought to be calibrated with suitable mock catalogs, that are offered as benchmarks.Comment: 8 pages LaTeX, 8 embedded figures. paspconf.sty. Higher quality figs from ftp://alf.fiz.huji.ac.il/pub/dekel/vic99/ as adekel*_l.ps.gz (*=1-8). In "Cosmic Flows: Towards an Understanding of Large-Scale Structure", eds S. Courteau, M.A. Strauss, & J.A. Willick, ASP Conf. Serie

An O^*(2.619^k) algorithm for 4-path vertex cover

In the 4-path vertex cover problem, the input is an undirected graph $G$ and an integer $k$. The goal is to decide whether there is a set of vertices $S$ of size at most $k$ such that every path with 4 vertices in $G$ contains at least one vertex of $S$. In this paper we give a parameterized algorithm for 4-path vertex cover whose time complexity is $O^*(2.619^k)$

Dynamics of Cosmic Flows

CONTENTS: 1. INTRODUCTION 2. GRAVITATIONAL INSTABILITY 3. MEASURING PECULIAR VELOCITIES 4. ANALYSIS OF OBSERVED PECULIAR VELOCITIES 5. PREDICTED MOTIONS FROM THE GALAXY DISTRIBUTION 6. TESTING BASIC HYPOTHESES 7. THE INITIAL FLUCTUATIONS 8. THE VALUE OF OMEGA 9. DISCUSSION: ARE THE HYPOTHESES JUSTIFIED? REFERENCESComment: A review for Ann. Rev. of Astron. and Astrophys. 32 (October 1994). 46 pages, 10 figures built-in, compressed and uuencoded PostScript (1.58 Mbyte). (Also available by anonymous ftp from venus.huji.ac.il as pub/dekel/reviews/annrev9.uu, or text and figures separately as annrev7.uu with fig*.ps) (HUJI-AST-94-002

Algebraic Curves for Factorized String Solutions

We show how to construct an algebraic curve for factorized string solution in the context of the AdS/CFT correspondence. We define factorized solutions to be solutions where the flat-connection becomes independent of one of the worldsheet variables by a similarity transformation with a matrix $S$ satisfying $S^{-1}d S=const$. Using the factorization property we construct a well defined Lax operator and an associated algebraic curve. The construction procedure is local and does not require the introduction of a monodromy matrix. The procedure can be applied for string solutions with any boundary conditions. We study the properties of the curve and give several examples for the application of the procedure.Comment: 22 page