Maximum Independent Sets in Subcubic Graphs: New Results

The maximum independent set problem is known to be NP-hard in the class of subcubic graphs, i.e. graphs of vertex degree at most 3. We present a polynomial-time solution in a subclass of subcubic graphs generalizing several previously known results

Potential for measurement of the tensor magnetic polarizability of the deuteron in storage ring experiments

General formulas describing deuteron spin dynamics in storage rings with allowance for the tensor electric and magnetic polarizabilities are derived. It is found that an initially tensor-polarized deuteron beam can acquire a final horizontal vector polarization of the order of 1%. This effect allows one to measure the tensor magnetic polarizability of the deuteron in storage ring experiments. We also confirm an existence of the effect found by Baryshevsky and Gurinovich, hep-ph/0506135 and Baryshevsky, hep-ph/0510158; hep-ph/0603191 that the tensor magnetic polarizability of the deuteron causes the spin rotation with two frequencies and experiences beating for polarized deuteron beams in storage rings.Comment: Corrected text, 8 page

Maximum Independent Sets in Subcubic Graphs: New Results

International audienceWe consider the complexity of the classical Independent Set problem on classes of subcubic graphs characterized by a finite set of forbidden induced subgraphs. It is well-known that a necessary condition for Independent Set to be tractable in such a class (unless P=NP) is that the set of forbidden induced subgraphs includes a subdivided star S k,k,k , for some k. Here, S k,k,k is the graph obtained by taking three paths of length k and identifying one of their endpoints. It is an interesting open question whether this condition is also sufficient: is Independent Set tractable on all hereditary classes of subcu-bic graphs that exclude some S k,k,k ? A positive answer to this question would provide a complete classification of the complexity of Independent Set on all classes of subcubic graphs characterized by a finite set of forbidden induced subgraphs. The best currently known result of this type is tractability for S2,2,2-free graphs. In this paper we generalize this result by showing that the problem remains tractable on S 2,k,k-free graphs, for any fixed k. Along the way, we show that subcubic Independent Set is tractable for graphs excluding a type of graph we call an "apple with a long stem", generalizing known results for apple-free graphs

First test of a partial Siberian snake for acceleration of polarized protons

We recently studied the first acceleration of a spin‐polarized proton beam through a depolarizing resonance using a partial Siberian snake. We accelerated polarized protons from 95 to 140 MeV with a constant 10% partial Siberian snake obtained using rampable solenoids. The 10% partial snake suppressed all observable depolarization during acceleration due to the Gγ=2 imperfection depolarizing resonance which occurred near 108 MeV. However, 20% and 30% partial Siberian snakes apparently moved an intrinsic depolarizing resonance, normally near 177 MeV, into our energy range; this caused some interesting, although not‐yet‐fully understood, depolarization. © 1995 American Institute of Physics.Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/87483/2/85_1.pd

Do black holes radiate?

The prediction that black holes radiate due to quantum effects is often considered one of the most secure in quantum field theory in curved space-time. Yet this prediction rests on two dubious assumptions: that ordinary physics may be applied to vacuum fluctuations at energy scales increasing exponentially without bound; and that quantum-gravitational effects may be neglected. Various suggestions have been put forward to address these issues: that they might be explained away by lessons from sonic black hole models; that the prediction is indeed successfully reproduced by quantum gravity; that the success of the link provided by the prediction between black holes and thermodynamics justifies the prediction. This paper explains the nature of the difficulties, and reviews the proposals that have been put forward to deal with them. None of the proposals put forward can so far be considered to be really successful, and simple dimensional arguments show that quantum-gravitational effects might well alter the evaporation process outlined by Hawking. Thus a definitive theoretical treatment will require an understanding of quantum gravity in at least some regimes. Until then, no compelling theoretical case for or against radiation by black holes is likely to be made. The possibility that non-radiating "mini" black holes exist should be taken seriously; such holes could be part of the dark matter in the Universe. Attempts to place observational limits on the number of "mini" black holes (independent of the assumption that they radiate) would be most welcome.Comment: review article, 80 pp., 3 included eps figures, IOP macros (included

Utilization and control of ecological interactions in polymicrobial infections and community-based microbial cell factories

Microbial activities are most often shaped by interactions between co-existing microbes within mixed-species communities. Dissection of the molecular mechanisms of species interactions within communities is a central issue in microbial ecology, and our ability to engineer and control microbial communities depends, to a large extent, on our knowledge of these interactions. This review highlights the recent advances regarding molecular characterization of microbe-microbe interactions that modulate community structure, activity, and stability, and aims to illustrate how these findings have helped us reach an engineering-level understanding of microbial communities in relation to both human health and industrial biotechnology