Disjoint paths in tournaments

Given k   pairs of vertices (_si,_ti)$(s_i,t_i)$(1≤i≤k)$(1\le i\le k)$ of a digraph G, how can we test whether there exist k   vertex-disjoint directed paths from _si$s_i$ to _ti$t_i$ for 1≤i≤k$1\le i\le k$? This is NP-complete in general digraphs, even for k=2$k=2$ [2], but for k=2$k=2$ there is a polynomial-time algorithm when G is a tournament (or more generally, a semicomplete digraph), due to Bang-Jensen and Thomassen [1]. Here we prove that for all fixed k there is a polynomial-time algorithm to solve the problem when G is semicomplete.     

Chiral recognition in solution and the gas phase. Experimental and theoretical studies of aromatic D- and L-amino acid–Cu(II)–chiragen complexes Jennifer L. Seymour František Tureček Andrei V. Malkov Pavel Kočovský Journal of Mass Spectrometry 2004; 39: 1044–1052

The original article to which this Erratum refers was published in Journal of Mass Spectrometry 2004; 39: 1044–1052.     

Calorimetric investigations on mound-building birds

Megapodes, and mound-building birds of the Pacific, incubate their eggs underground where the heat is supplied by organic decomposition, solar radiation, or geothermal sources. The incubation biology of the Australian mound builders has been examined from the standpoints of (1) the energetic requirements of malleefowl (Leipoa ocellata) to construct and maintain incubation mounds and (2) the physics, physiology, and behavior concerning mound thermoregulation of the brush turkey (Alectura lathami).

The energetic cost of mound tending in malleefowl is estimated by indirect calorimetry. The power required for digging into the mound to reach the eggs is approximately 20 W, or 3.8 times the basal metabolic rate of the bird. About 850 kg of sand has to be removed and replaced on the mound every time it is opened, a task requiring about 5 h. The overall energy investment for incubation for the entire 9 month season is 2.5 times that expected in similarly sized birds.

Brush turkey mounds become homeothermic because of (1) the high thermal inertia of their 3–11 t mass and (2) a stable equilibrium that is reached between heat production and heat loss. The mound tends to seek the equilibrium, but the bird adjusts the temperature by subtle manipulation of the mound. At an equilibrium temperature of 33°C, the mound produces about 110 W. Empirical data from natural mounds, set in the context of a numerical model of heat production and heat flux in the mound, indicate that equilibrium temperature is extremely sensitive to ambient temperature and mound size, but not water content. Wet or dry mounds can maintain appropriate incubation temperature, but the dry ones have low thermal conductivity, retain the heat well, and minimize the amount of forest litter collected during the incubation season.     

Exact Solutions for Large Amplitude Waves in Dispersive and Dissipative Systems

This paper describes some applications of a transformation which takes a system of two, first order, quasilinear, partial differential equations in two dependent and two independent variables into a similar system. Typically, the equations govern wave propagation in dispersive and dissipative systems. It is shown that certain nonlinear equations which are of current practical interest can be transformed into linear equations.     

Laterally stabilized complexes of DNA with linear reducible polycations: strategy for triggered intracellular activation of DNA delivery vectors.

Target-specific DNA delivery requires vectors that combine stability in the biological milieu, receptor-mediated uptake into target cells, and intracellular activation to mediate transgene expression. This is achieved here using polymer-coated vectors based on plasmid DNA complexed with a reductively degradable polycation (RPC), designed for intercellular degradation. The RPC were prepared by oxidation of the terminal cysteinyl thiol groups of Cys(Lys)10Cys. The complexes were coated and surface-cross-linked using multivalent reactive copolymers of N-(2-hydroxypropyl)methacrylamide (PHPMA), providing a unique combination of steric and reversible lateral stabilization, known to promote extended circulation in the bloodstream. Coated complexes containing RPC exhibited lateral stabilization that was reversible by treatment with 2.5 mM dithiothreitol, releasing free DNA after incubation with a polyanion. In contrast, coated complexes containing nonreducible poly(l-lysine) (PLL) were not destabilized by reduction. The biological usefulness of this trigger mechanism was examined by measuring transfection activity in human retinoblast 911 cells of coated complexes, based on PLL or RPC, targeted to cell surface receptors by covalent linkage of basic fibroblast growth factor. The levels of transgene expression observed for RPC-based targeted vectors indicated efficient intracellular activation, authenticating the concept that lateral stabilization introduced by surface coating with PHPMA can be reversed by intracellular reduction.     

Counting negative eigenvalues of a Hilbert-Schmidt operator via sign changes of a determinant

In this paper a continuous analogue of the Jacobi-Sturm rule for counting the number of negative eigenvalues of a Hermitian matrix is derived.     

Subgraphs of large connectivity and chromatic number in graphs of large chromatic number

For each pair k, m of natural numbers there exists a natural number f(k, m) such that every f(k, m)-chromatic graph contains a k-connected subgraph of chromatic number at least m.     

A counterexample to the rank-coloring conjecture

It has been conjectured by C. van Nuffelen that the chromatic number of any graph with at least one edge does not exceed the rank of its adjacency matrix. We give a counterexample, with chromatic number 32 and with an adjacency matrix of rank 29.