Unambiguous one-loop quantum energies of 1+1 dimensional bosonic field configurations

We calculate one-loop quantum energies in a renormalizable self-interacting theory in one spatial dimension by summing the zero-point energies of small oscillations around a classical field configuration, which need not be a solution of the classical field equations. We unambiguously implement standard perturbative renormalization using phase shifts and the Born approximation. We illustrate our method by calculating the quantum energy of a soliton/antisoliton pair as a function of their separation. This energy includes an imaginary part that gives a quantum decay rate and is associated with a level crossing in the solutions to the classical field equation in the presence of the source that maintains the soliton/antisoliton pair.Comment: Email correspondence to [email protected] ; 10 pages, 2 figures, REVTeX, BoxedEPS; v2: Fixed description of level crossing as a function of $x_0$; v3: Fixed numerical error in figure dat

Recent trends in Euclidean Ramsey theory

AbstractWe give a brief summary of several new results in Euclidean Ramsey theory, a subject which typically investigates properties of configurations in Euclidean space which are preserved under finite partitions of the space

Commercially Viable Bus Services Are Encouraged by Legislation in N.S.W., Australia

Institute of Transport and Logistics Studies. Business School. The University of Sydney

Approximate Self-Assembly of the Sierpinski Triangle

The Tile Assembly Model is a Turing universal model that Winfree introduced in order to study the nanoscale self-assembly of complex (typically aperiodic) DNA crystals. Winfree exhibited a self-assembly that tiles the first quadrant of the Cartesian plane with specially labeled tiles appearing at exactly the positions of points in the Sierpinski triangle. More recently, Lathrop, Lutz, and Summers proved that the Sierpinski triangle cannot self-assemble in the "strict" sense in which tiles are not allowed to appear at positions outside the target structure. Here we investigate the strict self-assembly of sets that approximate the Sierpinski triangle. We show that every set that does strictly self-assemble disagrees with the Sierpinski triangle on a set with fractal dimension at least that of the Sierpinski triangle (roughly 1.585), and that no subset of the Sierpinski triangle with fractal dimension greater than 1 strictly self-assembles. We show that our bounds are tight, even when restricted to supersets of the Sierpinski triangle, by presenting a strict self-assembly that adds communication fibers to the fractal structure without disturbing it. To verify this strict self-assembly we develop a generalization of the local determinism method of Soloveichik and Winfree

Contrasting effects of fluoroquinolone antibiotics on the expression of the collagenases, matrix metalloproteinases (MMP)-1 and -13, in human tendon-derived cells

Fluoroquinolone antibiotics may cause tendon pain and rupture. We reported previously that the fluoroquinolone ciprofloxacin potentiated interleukin (IL)-1ß-stimulated expression of matrix metalloproteinases (MMP)-3 and MMP-1 in human tendon-derived cells. We have now tested additional fluoroquinolones and investigated whether they have a similar effect on expression of MMP-13. Tendon cells were incubated for two periods of 48?h with or without fluoroquinolones and IL-1ß. Total ribonucleic acid (RNA) was assayed for MMP messenger RNA by relative quantitative reverse transcriptase polymerase chain reaction, with normalization for glyceraldehyde-3-phosphate dehydrogenase mRNA. Samples of supernatant medium were assayed for MMP output by activity assays. MMP-13 was expressed by tendon cells at lower levels than MMP-1, and was stimulated typically 10- to 100-fold by IL-1ß. Ciprofloxacin, norfloxacin and ofloxacin each reduced both basal and stimulated expression of MMP-13 mRNA. In contrast, ciprofloxacin and norfloxacin increased basal and IL-1ß-stimulated MMP-1 mRNA expression. Both the inhibition of MMP-13 and the potentiation of MMP-1 expression by fluoroquinolones were accompanied by corresponding changes in IL-1ß-stimulated MMP output. The non-fluorinated quinolone nalidixic acid had lesser or no effects. Fluoroquinolones show contrasting effects on the expression of the two collagenases MMP-1 and MMP-13, indicating specific effects on MMP gene regulation

On packing squares with equal squares

AbstractThe following problem arises in connection with certain multidimensional stock cutting problems:How many nonoverlapping open unit squares may be packed into a large square of side α?Of course, if α is a positive integer, it is trivial to see that α2 unit squares can be succesfully packed. However, if α is not an integer, the problem becomes much more complicated. Intuitively, one feels that for α = N + (1100), say (where N is an integer), one should pack N2 unit squares in the obvious way and surrender the uncovered border area (which is about α50) as unusable waste. After all, how could it help to place the unit squares at all sorts of various skew angles?In this note, we show how it helps. In particular, we prove that we can always keep the amount of uncovered area down to at most proportional to α711, which for large α is much less than the linear waste produced by the “natural” packing above

A Heavy Fermion Can Create a Soliton: A 1+1 Dimensional Example

We show that quantum effects can stabilize a soliton in a model with no soliton at the classical level. The model has a scalar field chirally coupled to a fermion in 1+1 dimensions. We use a formalism that allows us to calculate the exact one loop fermion contribution to the effective energy for a spatially varying scalar background. This energy includes the contribution from counterterms fixed in the perturbative sector of the theory. The resulting energy is therefore finite and unambiguous. A variational search then yields a fermion number one configuration whose energy is below that of a single free fermion.Comment: 10 pages, RevTeX, 2 figures composed from 4 .eps files; v2: fixed minor errors, added reference; v3: corrected reference added in v

The Casimir Effect for Fermions in One Dimension

We study the Casimir problem for a fermion coupled to a static background field in one space dimension. We examine the relationship between interactions and boundary conditions for the Dirac field. In the limit that the background becomes concentrated at a point (a ``Dirac spike'') and couples strongly, it implements a confining boundary condition. We compute the Casimir energy for a masslike background and show that it is finite for a stepwise continuous background field. However the total Casimir energy diverges for the Dirac spike. The divergence cannot be removed by standard renormalization methods. We compute the Casimir energy density of configurations where the background field consists of one or two sharp spikes and show that the energy density is finite except at the spikes. Finally we define and compute an interaction energy density and the force between two Dirac spikes as a function of the strength and separation of the spikes.Comment: 18 pages, 6 figure

On the complexity of the multiple stack TSP, kSTSP

The multiple Stack Travelling Salesman Problem, STSP, deals with the collect and the deliverance of n commodities in two distinct cities. The two cities are represented by means of two edge-valued graphs (G1,d2) and (G2,d2). During the pick-up tour, the commodities are stored into a container whose rows are subject to LIFO constraints. As a generalisation of standard TSP, the problem obviously is NP-hard; nevertheless, one could wonder about what combinatorial structure of STSP does the most impact its complexity: the arrangement of the commodities into the container, or the tours themselves? The answer is not clear. First, given a pair (T1,T2) of pick-up and delivery tours, it is polynomial to decide whether these tours are or not compatible. Second, for a given arrangement of the commodities into the k rows of the container, the optimum pick-up and delivery tours w.r.t. this arrangement can be computed within a time that is polynomial in n, but exponential in k. Finally, we provide instances on which a tour that is optimum for one of three distances d1, d2 or d1+d2 lead to solutions of STSP that are arbitrarily far to the optimum STSP