arXiv subjects

S. Bilke

Publications and source records attributed to S. Bilke.

13 recordsLinked to original sources

arXiv2003

Probabilistic estimation of microarray data reliability and underlying gene expression

Background: The availability of high throughput methods for measurement of mRNA concentrations makes the reliability of conclusions drawn from the data and global quality control of samples and hybridization important issues. We address these issues by an information theoretic approach, applied to discretized expression values in replicated gene expression data. Results: Our approach yields a quantitative measure of two important parameter classes: First, the probability $P(σ| S)$ that a gene is in the biological state $σ$ in a certain variety, given its observed expression $S$ in the samples of that variety. Second, sample specific error probabilities which serve as consistency indicators of the measured samples of each variety. The method and its limitations are tested on gene expression data for developing murine B-cells and a $t$-test is used as reference. On a set of known genes it performs better than the $t$-test despite the crude discretization into only two expression levels. The consistency indicators, i.e. the error probabilities, correlate well with variations in the biological material and thus prove efficient. Conclusions: The proposed method is effective in determining differential gene expression and sample reliability in replicated microarray data. Already at two discrete expression levels in each sample, it gives a good explanation of the data and is comparable to standard techniques.

q-bio.QM↗

arXiv2001

Stability of the Kauffman Model

Random Boolean networks, the Kauffman model, are revisited by means of a novel decimation algorithm, which reduces the networks to their dynamical cores. The average size of the removed part, the stable core, grows approximately linearly with N, the number of nodes in the original networks. We show that this can be understood as the percolation of the stability signal in the network. The stability of the dynamical core is investigated and it is shown that this core lacks the well known stability observed in full Kauffman networks. We conclude that, somewhat counter-intuitive, the remarkable stability of Kauffman networks is generated by the dynamics of the stable core. The decimation method is also used to simulate large critical Kauffman networks. For networks up to N=32 we perform full enumeration studies. Strong evidence is provided for that the number of limit cycles grows linearly with N. This result is in sharp contrast to the often cited $\sqrt{N}$ behavior.

cond-mat.stat-mech↗

arXiv2001

Topological Properties of Citation and Metabolic Networks

Topological properties of "scale-free" networks are investigated by determining their spectral dimensions $d_S$, which reflect a diffusion process in the corresponding graphs. Data bases for citation networks and metabolic networks together with simulation results from the growing network model \cite{barab} are probed. For completeness and comparisons lattice, random, small-world models are also investigated. We find that $d_S$ is around 3 for citation and metabolic networks, which is significantly different from the growing network model, for which $d_S$ is approximately 7.5. This signals a substantial difference in network topology despite the observed similarities in vertex order distributions. In addition, the diffusion analysis indicates that whereas the citation networks are tree-like in structure, the metabolic networks contain many loops.

cond-mat.dis-nn↗

arXiv1999

Hypercubic Random Surfaces with Extrinsic Curvature

We analyze a model of hypercubic random surfaces with an extrinsic curvature term in the action. We find a first order phase transition at finite coupling separating a branched polymer from a stable flat phase.

hep-lat↗

arXiv1998

Simulating Four-Dimensional Simplicial Gravity using Degenerate Triangulations

We extend a model of four-dimensional simplicial quantum gravity to include degenerate triangulations in addition to combinatorial triangulations traditionally used. Relaxing the constraint that every 4-simplex is uniquely defined by a set of five distinct vertexes, we allow triangulations containing multiply connected simplexes and distinct simplexes defined by the same set of vertexes. We demonstrate numerically that including degenerated triangulations substantially reduces the finite-size effects in the model. In particular, we provide a strong numerical evidence for an exponential bound on the entropic growth of the ensemble of degenerate triangulations, and show that a discontinuous crumpling transition is already observed on triangulations of volume N_4 ~= 4000.

hep-lat↗

arXiv1998

Simulating 4D Simplicial Gravity including Degenerate Triangulations

We extend simulations of simplicial gravity in four dimensions to include {\it degenerate} triangulations and demonstrate that using this ensemble the geometric finite-size effects are much reduced. We provide strong numerical evidence for the existence of an exponential bound on the entropy of the model and establish that the phase structure is identical to that of a corresponding model restricted to an ensemble of combinatorial triangulations.

hep-lat↗

arXiv1998

The Strong-Coupling Expansion in Simplicial Quantum Gravity

We construct the strong-coupling series in 4d simplicial quantum gravity up to volume 38. It is used to calculate estimates for the string susceptibility exponent gamma for various modifications of the theory. It provides a very efficient way to get a first view of the phase structure of the models.

hep-lat↗

arXiv1998

4d Simplicial Quantum Gravity: Matter Fields and the Corresponding Effective Action

Four-dimensional simplicial quantum gravity is modified either by coupling it to U(1) gauge fields or by introducing a measure weighted by the orders of the triangles. Strong coupling expansion and Monte Carlo simulations are used. Although the two modifications of the standard pure-gravity model are apparently very distinct, they produce strikingly similar results, as far as the geometry of random manifolds is concerned. In particular, for an appropriate choice of couplings, the branched polymer phase is replaced by a crinkled phase, characterized by the susceptibility exponent $γ< 0$ and the fractal dimension $d_H > 2$. The quasi-equivalence between the two models is exploited to get further insight into the extended phase diagram of the theory.

hep-lat↗

arXiv1997

4d Simplicial Quantum Gravity Interacting with Gauge Matter Fields

The effect of coupling non-compact $U(1)$ gauge fields to four dimensional simplicial quantum gravity is studied using strong coupling expansions and Monte Carlo simulations. For one gauge field the back-reaction of the matter on the geometry is weak. This changes, however, as more matter fields are introduced. For more than two gauge fields the degeneracy of random manifolds into branched polymers does not occur, and the branched polymer phase seems to be replaced by a new phase with a negative string susceptibility exponent $γ$ and fractal dimension $d_H \approx 4$.

hep-lat↗

arXiv1997

Universality of hypercubic random surfaces

We study universality properties of the Weingarten hyper-cubic random surfaces. Since a long time ago the model with a local restriction forbidding surface self-bendings has been thought to be in a different universality class from the unrestricted model defined on the full set of surfaces. We show that both models in fact belong to the same universality class with the entropy exponent gamma = 1/2 and differ by finite size effects which are much more pronounced in the restricted model.

hep-th↗

arXiv1996

Topology in 4D simplicial quantum gravity

We simulate 4d simplicial gravity for three topologis S4, S3xS1, (S1)^4 and show that the free energy for these three fixed topology ensembles is the same in the thermodynamic limit. We show, that the next-to-leading order corrections, at least away from the critical point, can be described by kinematic sources.

hep-lat↗

arXiv1996

Phase transition and topology in 4d simplicial gravity

We present data indicating that the recent evidence for the phase transition being of first order does not result from a breakdown of the ergodicity of the algorithm. We also present data showing that the thermodynamical limit of the model is independent of topology.

hep-lat↗

arXiv1994

Simplicial Quantum Gravity on a Computer

We describe a method of Monte-Carlo simulations of simplicial quantum gravity coupled to matter fields. We concentrate mainly on the problem of implementing effectively the random, dynamical triangulation and building in a detailed-balance condition into the elementary transformations of the triangulation. We propose a method of auto-tuning the parameters needed to balance simulations of the canonical ensemble. This method allows us to prepare a whole set of jobs and therefore is very useful in systematic determining the phase diagram in two dimensional coupling space. It is of particular importance when the jobs are run on a parallel machine.

hep-lat↗