06051 Abstracts Collection -- Kolmogorov Complexity and Applications

From 29.01.06 to 03.02.06, the Dagstuhl Seminar 06051 ``Kolmogorov Complexity and Applications\u27\u27 was held in the International Conference and Research Center (IBFI), Schloss Dagstuhl. During the seminar, several participants presented their current research, and ongoing work and open problems were discussed. Abstracts of the presentations given during the seminar as well as abstracts of seminar results and ideas are put together in this paper. The first section describes the seminar topics and goals in general. Links to extended abstracts or full papers are provided, if available

Explicit Formulas for Neumann Coefficients in the Plane-Wave Geometry

We obtain explicit formulas for the Neumann coefficients and associated quantities that appear in the three-string vertex for type IIB string theory in a plane-wave background, for any value of the mass parameter mu. The derivation involves constructing the inverse of a certain infinite-dimensional matrix, in terms of which the Neumann coefficients previously had been written only implicitly. We derive asymptotic expansions for large mu and find unexpectedly simple results, which are valid to all orders in 1/mu. Using BMN duality, these give predictions for certain gauge theory quantities to all orders in the modified 't Hooft coupling lambda'. A specific example is presented.Comment: 28 pages, 2 figures, v2: reference added, new comments and appendix, typos fixed in eqs. (86) and (89

On the spatial Markov property of soups of unoriented and oriented loops

We describe simple properties of some soups of unoriented Markov loops and of some soups of oriented Markov loops that can be interpreted as a spatial Markov property of these loop-soups. This property of the latter soup is related to well-known features of the uniform spanning trees (such as Wilson's algorithm) while the Markov property of the former soup is related to the Gaussian Free Field and to identities used in the foundational papers of Symanzik, Nelson, and of Brydges, Fr\"ohlich and Spencer or Dynkin, or more recently by Le Jan

On light-cone SFT contact terms in a plane wave

Testing the BMN correspondence at non-zero string coupling g_s requires a one-loop string field theory calculation. At order g_s^2, matrix elements of the light-cone string field theory Hamiltonian between single-string states receive two contributions: the iterated cubic interaction, and a contact term {Q, Q} whose presence is dictated by supersymmetry. In this paper we calculate the leading large mu p^+ alpha' contribution from both terms for the set of intermediate states with two string excitations. We find precise agreement with the basis-independent order g_2^2 results from gauge theory.Comment: 15 pages, 1 figur

Recovery of Methanotrophic Activity Is Not Reflected in the Methane-Driven Interaction Network after Peat Mining

Aerobic methanotrophs are crucial in ombrotrophic peatlands, driving the methane and nitrogen cycles. Peat mining adversely affects methanotrophs, but activity and community composition/abundances may recover after restoration. Considering that the methanotrophic activity and growth are significantly stimulated in the presence of other microorganisms, the methane-driven interaction network, which encompasses methanotrophs and nonmethanotrophs (i.e., the methanotrophic interactome), may also be relevant in conferring community resilience. Yet, little is known of the methanotrophic interactome's response to and recovery from disturbances. Here, we determined the recovery of the methanotrophic interactome as inferred by a co-occurrence network analysis comparing pristine and restored peatlands. We coupled a DNA-based stable isotope probing (SIP) approach using [13C]CH4 to a co-occurrence network analysis derived from the 13C-enriched 16S rRNA gene sequences to relate the response in methanotrophic activity to the structuring of the interaction network. Methanotrophic activity and abundances recovered after peat restoration since 2000. “Methylomonaceae” taxa were the predominantly active methanotrophs in both peatlands, but the peatlands differed in the relative abundances of Methylacidiphilaceae and Methylocystis. However, bacterial community compositions were distinct in both peatlands. Likewise, the methanotrophic interactome was profoundly altered in the restored peatland. Structuring of the interaction network after peat mining resulted in the loss of complexity and modularity, indicating a less connected and efficient network, which may have consequences in the event of recurring/future disturbances. Therefore, determining the response of the methane-driven interaction network, in addition to relating methanotrophic activity to community composition/abundances, provided a more comprehensive understanding of the resilience of the methanotrophs

Langevin dynamics with a tilted periodic potential

We study a Langevin equation for a particle moving in a periodic potential in the presence of viscosity $\gamma$ and subject to a further external field $\alpha$. For a suitable choice of the parameters $\alpha$ and $\gamma$ the related deterministic dynamics yields heteroclinic orbits. In such a regime, in absence of stochastic noise both confined and unbounded orbits coexist. We prove that, with the inclusion of an arbitrarly small noise only the confined orbits survive in a sub-exponential time scale.Comment: 38 pages, 6 figure

Pure type I supergravity and DE(10)

We establish a dynamical equivalence between the bosonic part of pure type I supergravity in D=10 and a D=1 non-linear sigma-model on the Kac-Moody coset space DE(10)/K(DE(10)) if both theories are suitably truncated. To this end we make use of a decomposition of DE(10) under its regular SO(9,9) subgroup. Our analysis also deals partly with the fermionic fields of the supergravity theory and we define corresponding representations of the generalized spatial Lorentz group K(DE(10)).Comment: 28 page

Quasi Stable Black Holes at the Large Hadron Collider

We adress the production of black holes at LHC and their time evolution in space times with compactified space like extra dimensions. It is shown that black holes with life times of hundred fm/c can be produced at LHC. The possibility of quasi-stable remnants is discussed.Comment: 4 pages, 3 figures, typos removed, omitted factors included, accepted for publicatio

Higher Order Evaluation of the Critical Temperature for Interacting Homogeneous Dilute Bose Gases

We use the nonperturbative linear \delta expansion method to evaluate analytically the coefficients c_1 and c_2^{\prime \prime} which appear in the expansion for the transition temperature for a dilute, homogeneous, three dimensional Bose gas given by T_c= T_0 \{1 + c_1 a n^{1/3} + [ c_2^{\prime} \ln(a n^{1/3}) +c_2^{\prime \prime} ] a^2 n^{2/3} + {\cal O} (a^3 n)\}, where T_0 is the result for an ideal gas, a is the s-wave scattering length and n is the number density. In a previous work the same method has been used to evaluate c_1 to order-\delta^2 with the result c_1= 3.06. Here, we push the calculation to the next two orders obtaining c_1=2.45 at order-\delta^3 and c_1=1.48 at order-\delta^4. Analysing the topology of the graphs involved we discuss how our results relate to other nonperturbative analytical methods such as the self-consistent resummation and the 1/N approximations. At the same orders we obtain c_2^{\prime\prime}=101.4, c_2^{\prime \prime}=98.2 and c_2^{\prime \prime}=82.9. Our analytical results seem to support the recent Monte Carlo estimates c_1=1.32 \pm 0.02 and c_2^{\prime \prime}= 75.7 \pm 0.4.Comment: 29 pages, 3 eps figures. Minor changes, one reference added. Version in press Physical Review A (2002