Investigation of a Protein Complex Network

The budding yeast {\it Saccharomyces cerevisiae} is the first eukaryote whose genome has been completely sequenced. It is also the first eukaryotic cell whose proteome (the set of all proteins) and interactome (the network of all mutual interactions between proteins) has been analyzed. In this paper we study the structure of the yeast protein complex network in which weighted edges between complexes represent the number of shared proteins. It is found that the network of protein complexes is a small world network with scale free behavior for many of its distributions. However we find that there are no strong correlations between the weights and degrees of neighboring complexes. To reveal non-random features of the network we also compare it with a null model in which the complexes randomly select their proteins. Finally we propose a simple evolutionary model based on duplication and divergence of proteins.Comment: 19 pages, 9 figures, 1 table, to appear in Euro. Phys. J.

Ground State Properties of an Asymmetric Hubbard Model for Unbalanced Ultracold Fermionic Quantum Gases

In order to describe unbalanced ultracold fermionic quantum gases on optical lattices in a harmonic trap, we investigate an attractive ($U<0$) asymmetric ($t_\uparrow\neq t_\downarrow$) Hubbard model with a Zeeman-like magnetic field. In view of the model's spatial inhomogeneity, we focus in this paper on the solution at Hartree-Fock level. The Hartree-Fock Hamiltonian is diagonalized with particular emphasis on superfluid phases. For the special case of spin-independent hopping we analytically determine the number of solutions of the resulting self-consistency equations and the nature of the possible ground states at weak coupling. Numerical results for unbalanced Fermi-mixtures are presented within the local density approximation. In particular, we find a fascinating shell structure, involving normal and superfluid phases. For the general case of spin-dependent hopping we calculate the density of states and the possible superfluid phases in the ground state. In particular, we find a new magnetized superfluid phase.Comment: 9 pages, 5 figure

Transport of a quantum degenerate heteronuclear Bose-Fermi mixture in a harmonic trap

We report on the transport of mixed quantum degenerate gases of bosonic 87Rb and fermionic 40K in a harmonic potential provided by a modified QUIC trap. The samples are transported over a distance of 6 mm to the geometric center of the anti-Helmholtz coils of the QUIC trap. This transport mechanism was implemented by a small modification of the QUIC trap and is free of losses and heating. It allows all experiments using QUIC traps to use the highly homogeneous magnetic fields that can be created in the center of a QUIC trap and improves the optical access to the atoms, e.g., for experiments with optical lattices. This mechanism may be cascaded to cover even larger distances for applications with quantum degenerate samples.Comment: 7 pages, 8 figure

Euclidean versus hyperbolic congestion in idealized versus experimental networks

This paper proposes a mathematical justification of the phenomenon of extreme congestion at a very limited number of nodes in very large networks. It is argued that this phenomenon occurs as a combination of the negative curvature property of the network together with minimum length routing. More specifically, it is shown that, in a large n-dimensional hyperbolic ball B of radius R viewed as a roughly similar model of a Gromov hyperbolic network, the proportion of traffic paths transiting through a small ball near the center is independent of the radius R whereas, in a Euclidean ball, the same proportion scales as 1/R^{n-1}. This discrepancy persists for the traffic load, which at the center of the hyperbolic ball scales as the square of the volume, whereas the same traffic load scales as the volume to the power (n+1)/n in the Euclidean ball. This provides a theoretical justification of the experimental exponent discrepancy observed by Narayan and Saniee between traffic loads in Gromov-hyperbolic networks from the Rocketfuel data base and synthetic Euclidean lattice networks. It is further conjectured that for networks that do not enjoy the obvious symmetry of hyperbolic and Euclidean balls, the point of maximum traffic is near the center of mass of the network.Comment: 23 pages, 4 figure

Amicable pairs and aliquot cycles for elliptic curves

An amicable pair for an elliptic curve E/Q is a pair of primes (p,q) of good reduction for E satisfying #E(F_p) = q and #E(F_q) = p. In this paper we study elliptic amicable pairs and analogously defined longer elliptic aliquot cycles. We show that there exist elliptic curves with arbitrarily long aliqout cycles, but that CM elliptic curves (with j not 0) have no aliqout cycles of length greater than two. We give conjectural formulas for the frequency of amicable pairs. For CM curves, the derivation of precise conjectural formulas involves a detailed analysis of the values of the Grossencharacter evaluated at a prime ideal P in End(E) having the property that #E(F_P) is prime. This is especially intricate for the family of curves with j = 0.Comment: 53 page

DNA Renaturation at the Water-Phenol Interface

We study DNA adsorption and renaturation in a water-phenol two-phase system, with or without shaking. In very dilute solutions, single-stranded DNA is adsorbed at the interface in a salt-dependent manner. At high salt concentrations the adsorption is irreversible. The adsorption of the single-stranded DNA is specific to phenol and relies on stacking and hydrogen bonding. We establish the interfacial nature of a DNA renaturation at a high salt concentration. In the absence of shaking, this reaction involves an efficient surface diffusion of the single-stranded DNA chains. In the presence of a vigorous shaking, the bimolecular rate of the reaction exceeds the Smoluchowski limit for a three-dimensional diffusion-controlled reaction. DNA renaturation in these conditions is known as the Phenol Emulsion Reassociation Technique or PERT. Our results establish the interfacial nature of PERT. A comparison of this interfacial reaction with other approaches shows that PERT is the most efficient technique and reveals similarities between PERT and the renaturation performed by single-stranded nucleic acid binding proteins. Our results lead to a better understanding of the partitioning of nucleic acids in two-phase systems, and should help design improved extraction procedures for damaged nucleic acids. We present arguments in favor of a role of phenol and water-phenol interface in prebiotic chemistry. The most efficient renaturation reactions (in the presence of condensing agents or with PERT) occur in heterogeneous systems. This reveals the limitations of homogeneous approaches to the biochemistry of nucleic acids. We propose a heterogeneous approach to overcome the limitations of the homogeneous viewpoint

Production of a microbeam of slow highly charged ions with a tapered glass capillary

journal articl

Decomposition of semigroup algebras

Let A \subseteq B be cancellative abelian semigroups, and let R be an integral domain. We show that the semigroup ring R[B] can be decomposed, as an R[A]-module, into a direct sum of R[A]-submodules of the quotient ring of R[A]. In the case of a finite extension of positive affine semigroup rings we obtain an algorithm computing the decomposition. When R[A] is a polynomial ring over a field we explain how to compute many ring-theoretic properties of R[B] in terms of this decomposition. In particular we obtain a fast algorithm to compute the Castelnuovo-Mumford regularity of homogeneous semigroup rings. As an application we confirm the Eisenbud-Goto conjecture in a range of new cases. Our algorithms are implemented in the Macaulay2 package MonomialAlgebras.Comment: 12 pages, 2 figures, minor revisions. Package may be downloaded at http://www.math.uni-sb.de/ag/schreyer/jb/Macaulay2/MonomialAlgebras/html