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Marianne Bauer

Marianne Bauer appears in the imported research catalog. Authorship, coauthor and topic links are available while profile ownership is still unclaimed.

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Biological Physics cond-mat.quant-gas cond-mat.stat-mech cond-mat.str-el quant-ph Subcellular Processes

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preprint2026arXiv

Statistical mechanics for Scrabble predicts strategy, entropy and language

The crossword-like patterns of tiles in Scrabble form connected graphs of occupied sites on a square lattice. We find the most structureless description that reproduces means and covariances observed in real Scrabble games by adapting a maximum entropy approach to connected graphs. This pairwise model captures the data well, and predicts word-length statistics and geometric features of the Scrabble graphs correctly; in addition, the parameters of this model are interpretable and allow us to understand Scrabble playing strategies. Using this pairwise model, we calculate entropy differences and distinguishability of Scrabble graphs across languages, without having access to the letters on the tiles. Notably, we find that the entropy is predicted better by strategic gameplay -- such as word length on the board -- than lexicon size. Finally, we find that we can use the pairwise model to correctly assign Scrabble graphs to languages, avoiding explicit feature selection and at relatively low computational cost.

preprint2025arXiv

Weak transcription factor clustering at binding sites can facilitate information transfer from molecular signals

Transcription factor concentrations provide signals to cells that allow them to regulate gene expression to make correct cell fate decisions. Calculations for noise bounds in gene regulation suggest that clustering or cooperative binding of transcription factors decreases signal-to-noise ratios at binding sites. However, clustering of transcription factor molecules around binding sites is frequently observed. We develop two complementary models for clustering transcription factors at binding site sensors that allow us to study information transfer from a signal, the morphogen Bicoid, to a variable relevant to development, namely future cell fates. We find that weak cooperativity or clustering can allow for maximal information transfer, especially about the relevant variable. The timescale of measurement is crucial for predicting the optimal clustering strength: for short measurements, clustering allows for the implementation of a switch, while for long measurements, weak clustering allows the sensor to access maximal developmental information provided in a nonlinear signal. Finally, we find that clustering not only facilitates information maximization about the relevant variable, but also can allow the binding site sensors to achieve optimality in a related optimization goal, the information bottleneck (IB) bound. While the measurement time restricts the region on the information plane that is accessible, changes in clustering in conjunction with changes in the binding energy can shift the binding site along the optimal bound, and towards an optimal trade-off between obtaining information about the signal and obtaining relevant information.

preprint2014arXiv

Universal equation of state and pseudogap in the two-dimensional Fermi gas

We determine the thermodynamic properties and the spectral function for a homogeneous two-dimensional Fermi gas in the normal state using the Luttinger-Ward, or self-consistent T-matrix, approach. The density equation of state deviates strongly from that of the ideal Fermi gas even for moderate interactions, and our calculations suggest that temperature has a pronounced effect on the pressure in the crossover from weak to strong coupling, consistent with recent experiments. We also compute the superfluid transition temperature for a finite system in the crossover region. There is a pronounced pseudogap regime above the transition temperature: the spectral function shows a Bogoliubov-like dispersion with back-bending, and the density of states is significantly suppressed near the chemical potential. The contact density at low temperatures increases with interaction and compares well with both experiment and zero-temperature Monte Carlo results.

preprint2012arXiv

Dipolar Gases in Coupled One-Dimensional Lattices

We consider dipolar bosons in two tubes of one-dimensional lattices, where the dipoles are aligned to be maximally repulsive and the particle filling fraction is the same in each tube. In the classical limit of zero inter-site hopping, the particles arrange themselves into an ordered crystal for any rational filling fraction, forming a complete devil's staircase like in the single tube case. Turning on hopping within each tube then gives rise to a competition between the crystalline Mott phases and a liquid of defects or solitons. However, for the two-tube case, we find that solitons from different tubes can bind into pairs for certain topologies of the filling fraction. This provides an intriguing example of pairing that is purely driven by correlations close to a Mott insulator.