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- Z. Burda, Bengt G. Petersson, J. Tabaczek
- 2001

We study numerically the geometric properties of reduced super-symmetric non-compact SU(N) Yang-Mills integrals in D = 4 dimensions, for N = 2, 3,. .. , 8. We show that in the range of large eigenvalues of the matrices A Âµ , the original D-dimensional rotational symmetry is spontaneously broken and the dominating field configurations become one-dimensional,â€¦ (More)

- Piotr Bialas, Z. Burda
- 1996

We study grandâ€“canonical and canonical properties of the model of branched polymers proposed in [1]. We show that the model has a fourth order phase transition and calculate critical exponents. At the transition the exponent Î³ of the grand-canonical ensemble, analogous to the string susceptibility exponent of surface models, Î³ âˆ¼ 0.3237525... is the firstâ€¦ (More)

Permanent address: Institute of Physics, Jagellonian University, ul. Reymonta 4, 30-059 KrakÃ³w, Poland Laboratoire associÃ© au CNRS. whether this finding does not reflect a deficiency of the simulation set-up. As it is an important question, we have decided to check it in more detail. The result of this investigation is presented in sect. 2 of thisâ€¦ (More)

We simulate 4d simplicial gravity for three topologies S, S S and S S S S and show that the free energy for these three xed topology ensembles is the same in the thermodynamic limit N4 !1. We show, that the next-to-leading order corrections, at least away from the critical point, can be described by kinematic sources.

We discuss a general mechanism that drives the phase transition in the canonical ensemble in models of random geometries. As an example we consider a solvable model of branched polymers where the transition leading from treeâ€“ to bushâ€“like polymers relies on the occurrence of vertices with a large number of branches. The source of this transition is aâ€¦ (More)

- Piotr Bialas, Z. Burda
- 1996

Our earlier renormalization group study of simplicial gravity is extended and the evidence for the existence of an isolated ultra-violet fixed point is strengthened. A high statistics study of the volume and coupling constant dependence of the cumulants of the node distribution is carried out. It appears that the phase transition of the theory is of firstâ€¦ (More)

- Marcin ZagÃ³rski, Z. Burda, Bartlomiej Waclaw
- PLoS computational biology
- 2016

Evolutionary pathways describe trajectories of biological evolution in the space of different variants of organisms (genotypes). The probability of existence and the number of evolutionary pathways that lead from a given genotype to a better-adapted genotype are important measures of accessibility of local fitness optima and the reproducibility ofâ€¦ (More)

- J. K. Ochab, Z. Burda
- Physical review. E, Statistical, nonlinear, andâ€¦
- 2012

This paper compares a number of centrality measures and several (dis-)similarity matrices with which they can be defined. These matrices, which are used among others in community detection methods, represent quantities connected to enumeration of paths on a graph and to random walks. Relationships between some of these matrices are derived in the paper.â€¦ (More)

Gene regulatory networks typically have low in-degrees, whereby any given gene is regulated by few of the genes in the network. What mechanisms might be responsible for these low in-degrees? Starting with an accepted framework of the binding of transcription factors to DNA, we consider a simple model of gene regulatory dynamics. In this model, we show thatâ€¦ (More)

- Z. Burda
- 1995

A real space renormalization group technique, based on the hierarchical baby-universe structure of a typical dynamically triangulated manifold, is used to study scaling properties of 2d and 4d lattice quantum gravity. In 4d, the Î²-function is defined and calculated numerically. An evidence for the existence of an ultraviolet stable fixed point of the theoryâ€¦ (More)